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id="toc-Alternate_names-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Images" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Images"> <div class="vector-toc-text"> 1.2 Images </div> </a> <ul id="toc-Images-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Construction" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Construction"> <div class="vector-toc-text"> 1.3 Construction </div> </a> <ul id="toc-Construction-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Related_polytopes_and_honeycombs" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Related_polytopes_and_honeycombs"> <div class="vector-toc-text"> 1.4 Related polytopes and honeycombs </div> </a> <ul id="toc-Related_polytopes_and_honeycombs-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Rectified_1_32_polytope" class="vector-toc-list-item vector-toc-level-1 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class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Images_2"> <div class="vector-toc-text"> 2.3 Images </div> </a> <ul id="toc-Images_2-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> 3 See also </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> 4 Notes </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> 5 References </div> </a> <ul id="toc-References-sublist" 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class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Uniform polytope</div> <table class="wikitable" align="right" width="360" style="margin-left:1em;"> <tbody><tr align="center" valign="top"> <td colspan="2"><a href="/wiki/File:Up2_3_21_t0_E7.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Up2_3_21_t0_E7.svg/120px-Up2_3_21_t0_E7.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Up2_3_21_t0_E7.svg/180px-Up2_3_21_t0_E7.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/Up2_3_21_t0_E7.svg/240px-Up2_3_21_t0_E7.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> <a href="/wiki/3_21_polytope" title="3 21 polytope">321</a> <img src="//upload.wikimedia.org/wikipedia/commons/a/aa/CDel_nodea_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td colspan="2"><a href="/wiki/File:Up2_2_31_t0_E7.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Up2_2_31_t0_E7.svg/120px-Up2_2_31_t0_E7.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Up2_2_31_t0_E7.svg/180px-Up2_2_31_t0_E7.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Up2_2_31_t0_E7.svg/240px-Up2_2_31_t0_E7.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> <a href="/wiki/2_31_polytope" title="2 31 polytope">231</a> <img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/a/aa/CDel_nodea_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /> </td> <td colspan="2"><a href="/wiki/File:Up2_1_32_t0_E7.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Up2_1_32_t0_E7.svg/120px-Up2_1_32_t0_E7.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Up2_1_32_t0_E7.svg/180px-Up2_1_32_t0_E7.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/66/Up2_1_32_t0_E7.svg/240px-Up2_1_32_t0_E7.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> 132 <img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td></tr> <tr align="center" valign="top"> <td colspan="3"><a href="/wiki/File:Up2_3_21_t1_E7.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Up2_3_21_t1_E7.svg/150px-Up2_3_21_t1_E7.svg.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Up2_3_21_t1_E7.svg/225px-Up2_3_21_t1_E7.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/52/Up2_3_21_t1_E7.svg/300px-Up2_3_21_t1_E7.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> <a href="/wiki/Rectified_3_21_polytope" class="mw-redirect" title="Rectified 3 21 polytope">Rectified 321</a> <img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/a/aa/CDel_nodea_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td colspan="3"><a href="/wiki/File:Up2_3_21_t2_E7.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Up2_3_21_t2_E7.svg/150px-Up2_3_21_t2_E7.svg.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Up2_3_21_t2_E7.svg/225px-Up2_3_21_t2_E7.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/30/Up2_3_21_t2_E7.svg/300px-Up2_3_21_t2_E7.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> <a href="/wiki/Rectified_3_21_polytope" class="mw-redirect" title="Rectified 3 21 polytope">birectified 321</a> <img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/a/aa/CDel_nodea_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td></tr> <tr align="center" valign="top"> <td colspan="3"><a href="/wiki/File:Up2_2_31_t1_E7.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/18/Up2_2_31_t1_E7.svg/150px-Up2_2_31_t1_E7.svg.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/18/Up2_2_31_t1_E7.svg/225px-Up2_2_31_t1_E7.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/18/Up2_2_31_t1_E7.svg/300px-Up2_2_31_t1_E7.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> <a href="/wiki/Rectified_2_31_polytope" class="mw-redirect" title="Rectified 2 31 polytope">Rectified 231</a> <img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/a/aa/CDel_nodea_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td colspan="3" valign="center"><a href="/wiki/File:Up2_1_32_t1_E7.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Up2_1_32_t1_E7.svg/150px-Up2_1_32_t1_E7.svg.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Up2_1_32_t1_E7.svg/225px-Up2_1_32_t1_E7.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Up2_1_32_t1_E7.svg/300px-Up2_1_32_t1_E7.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> <a href="/wiki/Rectified_1_32_polytope" class="mw-redirect" title="Rectified 1 32 polytope">Rectified 132</a> <img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/9/97/CDel_branch_10.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td></tr> <tr valign="top"> <th colspan="6"><a href="/wiki/Orthogonal_projection" class="mw-redirect" title="Orthogonal projection">Orthogonal projections</a> in E7 <a href="/wiki/Coxeter_plane" class="mw-redirect" title="Coxeter plane">Coxeter plane</a> </th></tr></tbody></table> In 7-dimensional <a href="/wiki/Geometry" title="Geometry">geometry</a>, 132 is a <a href="/wiki/Uniform_polytope" title="Uniform polytope">uniform polytope</a>, constructed from the <a href="/wiki/E7_(mathematics)" title="E7 (mathematics)">E7</a> group. Its <a href="/wiki/Coxeter_symbol" class="mw-redirect" title="Coxeter symbol">Coxeter symbol</a> is 132, describing its bifurcating <a href="/wiki/Coxeter-Dynkin_diagram" class="mw-redirect" title="Coxeter-Dynkin diagram">Coxeter-Dynkin diagram</a>, with a single ring on the end of one of the 1-node sequences. The rectified 132 is constructed by points at the mid-edges of the 132. These polytopes are part of a family of 127 (27-1) convex <a href="/wiki/Uniform_7-polytope" title="Uniform 7-polytope">uniform polytopes in 7-dimensions</a>, made of <a href="/wiki/Uniform_polytope" title="Uniform polytope">uniform polytope</a> facets and <a href="/wiki/Vertex_figure" title="Vertex figure">vertex figures</a>, defined by all permutations of rings in this <a href="/wiki/Coxeter-Dynkin_diagram" class="mw-redirect" title="Coxeter-Dynkin diagram">Coxeter-Dynkin diagram</a>: <img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" />. <div style="clear:both;" class=""></div> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="1_32_polytope">1_32 polytope</h2>[<a href="/w/index.php?title=1_32_polytope&action=edit&section=1" title="Edit section: 1_32 polytope">edit</a>]</div> <table class="wikitable" align="right" style="margin-left:10px" width="280"> <tbody><tr> <th bgcolor="#e7dcc3" colspan="2">132 </th></tr> <tr> <td bgcolor="#e7dcc3">Type</td> <td><a href="/wiki/Uniform_7-polytope" title="Uniform 7-polytope">Uniform 7-polytope</a> </td></tr> <tr> <td bgcolor="#e7dcc3">Family</td> <td><a href="/wiki/Uniform_1_k2_polytope" title="Uniform 1 k2 polytope">1k2 polytope</a> </td></tr> <tr> <td bgcolor="#e7dcc3"><a href="/wiki/Schl%C3%A4fli_symbol" title="Schläfli symbol">Schläfli symbol</a></td> <td>{3,33,2} </td></tr> <tr> <td bgcolor="#e7dcc3"><a href="/wiki/Coxeter_symbol" class="mw-redirect" title="Coxeter symbol">Coxeter symbol</a></td> <td>132 </td></tr> <tr> <td bgcolor="#e7dcc3"><a href="/wiki/Coxeter_diagram" class="mw-redirect" title="Coxeter diagram">Coxeter diagram</a></td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td></tr> <tr> <td bgcolor="#e7dcc3">6-faces</td> <td>182: 56 <a href="/wiki/Gosset_1_22_polytope" class="mw-redirect" title="Gosset 1 22 polytope">122</a><a href="/wiki/File:Gosset_1_22_polytope.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Gosset_1_22_polytope.svg/30px-Gosset_1_22_polytope.svg.png" decoding="async" width="30" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Gosset_1_22_polytope.svg/45px-Gosset_1_22_polytope.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Gosset_1_22_polytope.svg/60px-Gosset_1_22_polytope.svg.png 2x" data-file-width="800" data-file-height="800" /></a> 126 <a href="/wiki/Demihexeract" class="mw-redirect" title="Demihexeract">131</a><a href="/wiki/File:Demihexeract_ortho_petrie.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/84/Demihexeract_ortho_petrie.svg/30px-Demihexeract_ortho_petrie.svg.png" decoding="async" width="30" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/84/Demihexeract_ortho_petrie.svg/45px-Demihexeract_ortho_petrie.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/84/Demihexeract_ortho_petrie.svg/60px-Demihexeract_ortho_petrie.svg.png 2x" data-file-width="800" data-file-height="800" /></a> </td></tr> <tr> <td bgcolor="#e7dcc3">5-faces</td> <td>4284: 756 <a href="/wiki/Demipenteract" class="mw-redirect" title="Demipenteract">121</a><a href="/wiki/File:Demipenteract_graph_ortho.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Demipenteract_graph_ortho.svg/25px-Demipenteract_graph_ortho.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Demipenteract_graph_ortho.svg/38px-Demipenteract_graph_ortho.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Demipenteract_graph_ortho.svg/50px-Demipenteract_graph_ortho.svg.png 2x" data-file-width="800" data-file-height="800" /></a> 1512 <a href="/wiki/Demipenteract" class="mw-redirect" title="Demipenteract">121</a><a href="/wiki/File:Demipenteract_graph_ortho.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Demipenteract_graph_ortho.svg/25px-Demipenteract_graph_ortho.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Demipenteract_graph_ortho.svg/38px-Demipenteract_graph_ortho.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Demipenteract_graph_ortho.svg/50px-Demipenteract_graph_ortho.svg.png 2x" data-file-width="800" data-file-height="800" /></a> 2016 <a href="/wiki/5-simplex" title="5-simplex">{34}</a><a href="/wiki/File:5-simplex_t0.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/5-simplex_t0.svg/25px-5-simplex_t0.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/5-simplex_t0.svg/38px-5-simplex_t0.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/5-simplex_t0.svg/50px-5-simplex_t0.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a> </td></tr> <tr> <td bgcolor="#e7dcc3">4-faces</td> <td>23688: 4032 <a href="/wiki/5-cell" title="5-cell">{33}</a><a href="/wiki/File:4-simplex_t0.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/4-simplex_t0.svg/25px-4-simplex_t0.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/4-simplex_t0.svg/38px-4-simplex_t0.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b9/4-simplex_t0.svg/50px-4-simplex_t0.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a> 7560 <a href="/wiki/16-cell" title="16-cell">111</a><a href="/wiki/File:Cross_graph_4.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Cross_graph_4.svg/25px-Cross_graph_4.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Cross_graph_4.svg/38px-Cross_graph_4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/32/Cross_graph_4.svg/50px-Cross_graph_4.svg.png 2x" data-file-width="228" data-file-height="228" /></a> 12096 <a href="/wiki/5-cell" title="5-cell">{33}</a><a href="/wiki/File:4-simplex_t0.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/4-simplex_t0.svg/25px-4-simplex_t0.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/4-simplex_t0.svg/38px-4-simplex_t0.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b9/4-simplex_t0.svg/50px-4-simplex_t0.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a> </td></tr> <tr> <td bgcolor="#e7dcc3">Cells</td> <td>50400: 20160 <a href="/wiki/Tetrahedron" title="Tetrahedron">{32}</a><a href="/wiki/File:3-simplex_t0.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/3-simplex_t0.svg/25px-3-simplex_t0.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/3-simplex_t0.svg/38px-3-simplex_t0.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e6/3-simplex_t0.svg/50px-3-simplex_t0.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a> 30240 <a href="/wiki/Tetrahedron" title="Tetrahedron">{32}</a><a href="/wiki/File:3-simplex_t0.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/3-simplex_t0.svg/25px-3-simplex_t0.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/3-simplex_t0.svg/38px-3-simplex_t0.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e6/3-simplex_t0.svg/50px-3-simplex_t0.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a> </td></tr> <tr> <td bgcolor="#e7dcc3">Faces</td> <td>40320 <a href="/wiki/Triangle" title="Triangle">{3}</a><a href="/wiki/File:2-simplex_t0.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/2-simplex_t0.svg/25px-2-simplex_t0.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/2-simplex_t0.svg/38px-2-simplex_t0.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/02/2-simplex_t0.svg/50px-2-simplex_t0.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a> </td></tr> <tr> <td bgcolor="#e7dcc3">Edges</td> <td>10080 </td></tr> <tr> <td bgcolor="#e7dcc3">Vertices</td> <td>576 </td></tr> <tr> <td bgcolor="#e7dcc3"><a href="/wiki/Vertex_figure" title="Vertex figure">Vertex figure</a></td> <td><a href="/wiki/Birectified_6-simplex" class="mw-redirect" title="Birectified 6-simplex">t2{35}</a> <a href="/wiki/File:6-simplex_t2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b3/6-simplex_t2.svg/25px-6-simplex_t2.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b3/6-simplex_t2.svg/38px-6-simplex_t2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b3/6-simplex_t2.svg/50px-6-simplex_t2.svg.png 2x" data-file-width="3200" data-file-height="3200" /></a> </td></tr> <tr> <td bgcolor="#e7dcc3"><a href="/wiki/Petrie_polygon" title="Petrie polygon">Petrie polygon</a></td> <td><a href="/wiki/Octadecagon" title="Octadecagon">Octadecagon</a> </td></tr> <tr> <td bgcolor="#e7dcc3"><a href="/wiki/Coxeter_group" title="Coxeter group">Coxeter group</a></td> <td><a href="/wiki/E7_(mathematics)" title="E7 (mathematics)">E7</a>, [33,2,1], order 2903040 </td></tr> <tr> <td bgcolor="#e7dcc3">Properties</td> <td><a href="/wiki/Convex_polytope" title="Convex polytope">convex</a> </td></tr></tbody></table> This polytope can <a href="/wiki/Honeycomb_(geometry)" title="Honeycomb (geometry)">tessellate</a> 7-dimensional space, with symbol 133, and Coxeter-Dynkin diagram, <img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" />. It is the <a href="/wiki/Voronoi_cell" class="mw-redirect" title="Voronoi cell">Voronoi cell</a> of the dual <a href="/wiki/E7_honeycomb" class="mw-redirect" title="E7 honeycomb">E7* lattice</a>.<a href="#cite_note-1">[1]</a> <div class="mw-heading mw-heading3"><h3 id="Alternate_names">Alternate names</h3>[<a href="/w/index.php?title=1_32_polytope&action=edit&section=2" title="Edit section: Alternate names">edit</a>]</div> <ul><li><a href="/wiki/Emanuel_Lodewijk_Elte" title="Emanuel Lodewijk Elte">Emanuel Lodewijk Elte</a> named it V576 (for its 576 vertices) in his 1912 listing of semiregular polytopes.<a href="#cite_note-2">[2]</a></li> <li><a href="/wiki/Coxeter" class="mw-redirect" title="Coxeter">Coxeter</a> called it 132 for its bifurcating <a href="/wiki/Coxeter-Dynkin_diagram" class="mw-redirect" title="Coxeter-Dynkin diagram">Coxeter-Dynkin diagram</a>, with a single ring on the end of the 1-node branch.</li> <li>Pentacontihexa-hecatonicosihexa-exon (Acronym lin) - 56-126 facetted polyexon (Jonathan Bowers)<a href="#cite_note-3">[3]</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Images">Images</h3>[<a href="/w/index.php?title=1_32_polytope&action=edit&section=3" title="Edit section: Images">edit</a>]</div> <table class="wikitable" width="600"> <caption><a href="/wiki/Coxeter_plane" class="mw-redirect" title="Coxeter plane">Coxeter plane</a> projections </caption> <tbody><tr> <th>E7 </th> <th>E6 / F4 </th> <th>B7 / A6 </th></tr> <tr valign="top" align="center"> <td><a href="/wiki/File:Up2_1_32_t0_E7.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Up2_1_32_t0_E7.svg/200px-Up2_1_32_t0_E7.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Up2_1_32_t0_E7.svg/300px-Up2_1_32_t0_E7.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/66/Up2_1_32_t0_E7.svg/400px-Up2_1_32_t0_E7.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> [18] </td> <td><a href="/wiki/File:Up2_1_32_t0_E6.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Up2_1_32_t0_E6.svg/200px-Up2_1_32_t0_E6.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Up2_1_32_t0_E6.svg/300px-Up2_1_32_t0_E6.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Up2_1_32_t0_E6.svg/400px-Up2_1_32_t0_E6.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> [12] </td> <td><a href="/wiki/File:Up2_1_32_t0_A6.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/18/Up2_1_32_t0_A6.svg/200px-Up2_1_32_t0_A6.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/18/Up2_1_32_t0_A6.svg/300px-Up2_1_32_t0_A6.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/18/Up2_1_32_t0_A6.svg/400px-Up2_1_32_t0_A6.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> [7x2] </td></tr> <tr> <th>A5 </th> <th>D7 / B6 </th> <th>D6 / B5 </th></tr> <tr valign="top" align="center"> <td><a href="/wiki/File:Up2_1_32_t0_A5.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Up2_1_32_t0_A5.svg/200px-Up2_1_32_t0_A5.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Up2_1_32_t0_A5.svg/300px-Up2_1_32_t0_A5.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Up2_1_32_t0_A5.svg/400px-Up2_1_32_t0_A5.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> [6] </td> <td><a href="/wiki/File:Up2_1_32_t0_D7.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Up2_1_32_t0_D7.svg/200px-Up2_1_32_t0_D7.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Up2_1_32_t0_D7.svg/300px-Up2_1_32_t0_D7.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Up2_1_32_t0_D7.svg/400px-Up2_1_32_t0_D7.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> [12/2] </td> <td><a href="/wiki/File:Up2_1_32_t0_D6.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Up2_1_32_t0_D6.svg/200px-Up2_1_32_t0_D6.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Up2_1_32_t0_D6.svg/300px-Up2_1_32_t0_D6.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/Up2_1_32_t0_D6.svg/400px-Up2_1_32_t0_D6.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> [10] </td></tr> <tr> <th>D5 / B4 / A4 </th> <th>D4 / B3 / A2 / G2 </th> <th>D3 / B2 / A3 </th></tr> <tr valign="top" align="center"> <td><a href="/wiki/File:Up2_1_32_t0_D5.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Up2_1_32_t0_D5.svg/200px-Up2_1_32_t0_D5.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Up2_1_32_t0_D5.svg/300px-Up2_1_32_t0_D5.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Up2_1_32_t0_D5.svg/400px-Up2_1_32_t0_D5.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> [8] </td> <td><a href="/wiki/File:Up2_1_32_t0_D4.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/Up2_1_32_t0_D4.svg/200px-Up2_1_32_t0_D4.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/Up2_1_32_t0_D4.svg/300px-Up2_1_32_t0_D4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/39/Up2_1_32_t0_D4.svg/400px-Up2_1_32_t0_D4.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> [6] </td> <td><a href="/wiki/File:Up2_1_32_t0_D3.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Up2_1_32_t0_D3.svg/200px-Up2_1_32_t0_D3.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Up2_1_32_t0_D3.svg/300px-Up2_1_32_t0_D3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/79/Up2_1_32_t0_D3.svg/400px-Up2_1_32_t0_D3.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> [4] </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Construction">Construction</h3>[<a href="/w/index.php?title=1_32_polytope&action=edit&section=4" title="Edit section: Construction">edit</a>]</div> It is created by a <a href="/wiki/Wythoff_construction" title="Wythoff construction">Wythoff construction</a> upon a set of 7 <a href="/wiki/Hyperplane" title="Hyperplane">hyperplane</a> mirrors in 7-dimensional space. The facet information can be extracted from its <a href="/wiki/Coxeter-Dynkin_diagram" class="mw-redirect" title="Coxeter-Dynkin diagram">Coxeter-Dynkin diagram</a>, <img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> Removing the node on the end of the 2-length branch leaves the <a href="/wiki/6-demicube" title="6-demicube">6-demicube</a>, 131, <img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> Removing the node on the end of the 3-length branch leaves the <a href="/wiki/1_22_polytope" title="1 22 polytope">122</a>, <img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> The <a href="/wiki/Vertex_figure" title="Vertex figure">vertex figure</a> is determined by removing the ringed node and ringing the neighboring node. This makes the <a href="/wiki/Birectified_6-simplex" class="mw-redirect" title="Birectified 6-simplex">birectified 6-simplex</a>, 032, <img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/a/aa/CDel_nodea_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> Seen in a <a href="/wiki/Configuration_(polytope)" title="Configuration (polytope)">configuration matrix</a>, the element counts can be derived by mirror removal and ratios of <a href="/wiki/Coxeter_group#Properties" title="Coxeter group">Coxeter group</a> orders.<a href="#cite_note-4">[4]</a> <table class="wikitable"> <tbody><tr> <th>E7</th> <th><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></th> <th>k-face</th> <th>fk</th> <th>f0</th> <th>f1</th> <th>f2</th> <th colspan="2">f3</th> <th colspan="3">f4</th> <th colspan="3">f5</th> <th colspan="2">f6</th> <th><a href="/wiki/Vertex_figure" title="Vertex figure">k-figures</a></th> <th>notes </th></tr> <tr align="right"> <td>A6</td> <td width="65"><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/4/4c/CDel_nodes_0x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td>( ) </td> <th>f0 </th> <td bgcolor="#ffe0ff">576</td> <td>35</td> <td>210</td> <td>140</td> <td>210</td> <td>35</td> <td>105</td> <td>105</td> <td>21</td> <td>42</td> <td>21</td> <td>7</td> <td>7</td> <td><a href="/wiki/Birectified_6-simplex" class="mw-redirect" title="Birectified 6-simplex">2r{3,3,3,3,3}</a></td> <td>E7/A6 = 72*8!/7! = 576 </td></tr> <tr align="right"> <td>A3A2A1</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7e/CDel_nodes_x1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td>{ } </td> <th>f1 </th> <td>2</td> <td bgcolor="#ffe0e0">10080</td> <td>12</td> <td>12</td> <td>18</td> <td>4</td> <td>12</td> <td>12</td> <td>6</td> <td>12</td> <td>3</td> <td>4</td> <td>3</td> <td>{3,3}x{3}</td> <td>E7/A3A2A1 = 72*8!/4!/3!/2 = 10080 </td></tr> <tr align="right"> <td>A2A2A1</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c5/CDel_branch_01.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td><a href="/wiki/Triangle" title="Triangle">{3}</a> </td> <th>f2 </th> <td>3</td> <td>3</td> <td bgcolor="#ffffe0">40320</td> <td>2</td> <td>3</td> <td>1</td> <td>6</td> <td>3</td> <td>3</td> <td>6</td> <td>1</td> <td>3</td> <td>2</td> <td>{ }∨{3}</td> <td>E7/A2A2A1 = 72*8!/3!/3!/2 = 40320 </td></tr> <tr align="right"> <td>A3A2</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b7/CDel_branch_01r.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td rowspan="2"><a href="/wiki/Tetrahedron" title="Tetrahedron">{3,3}</a> </td> <th rowspan="2">f3 </th> <td>4</td> <td>6</td> <td>4</td> <td bgcolor="#e0ffe0">20160</td> <td bgcolor="#e0ffe0">*</td> <td>1</td> <td>3</td> <td>0</td> <td>3</td> <td>3</td> <td>0</td> <td>3</td> <td>1</td> <td><a href="/wiki/Triangular_pyramid" class="mw-redirect" title="Triangular pyramid">{3}∨( )</a></td> <td>E7/A3A2 = 72*8!/4!/3! = 20160 </td></tr> <tr align="right"> <td>A3A1A1</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/CDel_branch_01l.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td>4</td> <td>6</td> <td>4</td> <td bgcolor="#e0ffe0">*</td> <td bgcolor="#e0ffe0">30240</td> <td>0</td> <td>2</td> <td>2</td> <td>1</td> <td>4</td> <td>1</td> <td>2</td> <td>2</td> <td><a href="/wiki/Phyllic_disphenoid" class="mw-redirect" title="Phyllic disphenoid">Phyllic disphenoid</a></td> <td>E7/A3A1A1 = 72*8!/4!/2/2 = 30240 </td></tr> <tr align="right"> <td>A4A2</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b7/CDel_branch_01r.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td><a href="/wiki/5-cell" title="5-cell">{3,3,3}</a> </td> <th rowspan="3">f4 </th> <td>5</td> <td>10</td> <td>10</td> <td>5</td> <td>0</td> <td bgcolor="#e0ffff">4032</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td>3</td> <td>0</td> <td>0</td> <td>3</td> <td>0</td> <td><a href="/wiki/Triangle" title="Triangle">{3}</a></td> <td>E7/A4A2 = 72*8!/5!/3! = 4032 </td></tr> <tr align="right"> <td>D4A1</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td><a href="/wiki/16-cell" title="16-cell">{3,3,4}</a> </td> <td>8</td> <td>24</td> <td>32</td> <td>8</td> <td>8</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">7560</td> <td bgcolor="#e0ffff">*</td> <td>1</td> <td>2</td> <td>0</td> <td>2</td> <td>1</td> <td rowspan="2"><a href="/wiki/Isosceles_triangle" title="Isosceles triangle">{ }∨( )</a></td> <td>E7/D4A1 = 72*8!/8/4!/2 = 7560 </td></tr> <tr align="right"> <td>A4A1</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/CDel_branch_01l.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td><a href="/wiki/5-cell" title="5-cell">{3,3,3}</a> </td> <td>5</td> <td>10</td> <td>10</td> <td>0</td> <td>5</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">12096</td> <td>0</td> <td>2</td> <td>1</td> <td>1</td> <td>2</td> <td>E7/A4A1 = 72*8!/5!/2 = 12096 </td></tr> <tr align="right"> <td>D5A1</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td rowspan="2"><a href="/wiki/5-demicube" title="5-demicube">h{4,3,3,3}</a> </td> <th rowspan="3">f5 </th> <td>16</td> <td>80</td> <td>160</td> <td>80</td> <td>40</td> <td>16</td> <td>10</td> <td>0</td> <td bgcolor="#e0e0ff">756</td> <td bgcolor="#e0e0ff">*</td> <td bgcolor="#e0e0ff">*</td> <td>2</td> <td>0</td> <td rowspan="3">{ }</td> <td>E7/D5A1 = 72*8!/16/5!/2 = 756 </td></tr> <tr align="right"> <td>D5</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td>16</td> <td>80</td> <td>160</td> <td>40</td> <td>80</td> <td>0</td> <td>10</td> <td>16</td> <td bgcolor="#e0e0ff">*</td> <td bgcolor="#e0e0ff">1512</td> <td bgcolor="#e0e0ff">*</td> <td>1</td> <td>1</td> <td>E7/D5 = 72*8!/16/5! = 1512 </td></tr> <tr align="right"> <td>A5A1</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/CDel_branch_01l.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td><a href="/wiki/5-simplex" title="5-simplex">{3,3,3,3,3} </a> </td> <td>6</td> <td>15</td> <td>20</td> <td>0</td> <td>15</td> <td>0</td> <td>0</td> <td>6</td> <td bgcolor="#e0e0ff">*</td> <td bgcolor="#e0e0ff">*</td> <td bgcolor="#e0e0ff">2016</td> <td>0</td> <td>2</td> <td>E7/A5A1 = 72*8!/6!/2 = 2016 </td></tr> <tr align="right"> <td>E6</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td><a href="/wiki/1_22_polytope" title="1 22 polytope">{3,32,2} </a> </td> <th rowspan="2">f6 </th> <td>72</td> <td>720</td> <td>2160</td> <td>1080</td> <td>1080</td> <td>216</td> <td>270</td> <td>216</td> <td>27</td> <td>27</td> <td>0</td> <td bgcolor="#ffe0ff">56</td> <td bgcolor="#ffe0ff">*</td> <td rowspan="2">( )</td> <td>E7/E6 = 72*8!/72/6! = 56 </td></tr> <tr align="right"> <td>D6</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td><a href="/wiki/6-demicube" title="6-demicube">h{4,3,3,3,3} </a> </td> <td>32</td> <td>240</td> <td>640</td> <td>160</td> <td>480</td> <td>0</td> <td>60</td> <td>192</td> <td>0</td> <td>12</td> <td>32</td> <td bgcolor="#ffe0ff">*</td> <td bgcolor="#ffe0ff">126</td> <td>E7/D6 = 72*8!/32/6! = 126 </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Related_polytopes_and_honeycombs">Related polytopes and honeycombs</h3>[<a href="/w/index.php?title=1_32_polytope&action=edit&section=5" title="Edit section: Related polytopes and honeycombs">edit</a>]</div> The 132 is third in a dimensional series of uniform polytopes and honeycombs, expressed by <a href="/wiki/Coxeter" class="mw-redirect" title="Coxeter">Coxeter</a> as 13k series. The next figure is the Euclidean honeycomb <a href="/wiki/1_33_honeycomb" title="1 33 honeycomb">133</a> and the final is a noncompact hyperbolic honeycomb, 134. <table class="wikitable"> <caption> 13k dimensional figures </caption> <tbody><tr> <th>Space </th> <th colspan="4">Finite </th> <th>Euclidean </th> <th>Hyperbolic </th></tr> <tr> <th>n </th> <th><a href="/wiki/Four-dimensional_space" title="Four-dimensional space">4</a> </th> <th><a href="/wiki/Five-dimensional_space" title="Five-dimensional space">5</a> </th> <th><a href="/wiki/Six-dimensional_space" title="Six-dimensional space">6</a> </th> <th><a href="/wiki/Seven-dimensional_space" title="Seven-dimensional space">7</a> </th> <th><a href="/wiki/Eight-dimensional_space" title="Eight-dimensional space">8</a> </th> <th><a href="/wiki/Nine-dimensional_space" class="mw-redirect" title="Nine-dimensional space">9</a> </th></tr> <tr style="text-align:center;"> <th><a href="/wiki/Coxeter_group" title="Coxeter group">Coxeter group</a> </th> <td>A3A1 </td> <td>A5 </td> <td>D6 </td> <td><a href="/wiki/E7_(mathematics)" title="E7 (mathematics)">E7</a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {E}}_{7}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {E}}_{7}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c251975c254e8e74513a013145d6ec2b0e5d016" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {E}}_{7}}">=E7+ </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {T}}_{8}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>T</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {T}}_{8}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/897b8ae2da2454683a692ed6b588068316ee4816" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.828ex; height:2.843ex;" alt="{\displaystyle {\bar {T}}_{8}}">=E7++ </td></tr> <tr style="text-align:center;"> <th><a href="/wiki/Coxeter%E2%80%93Dynkin_diagram" title="Coxeter–Dynkin diagram">Coxeter diagram</a> </th> <td><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/CDel_branch_01l.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td></tr> <tr style="text-align:center;"> <th><a href="/wiki/Coxeter_notation" title="Coxeter notation">Symmetry</a> </th> <td>[3−1,3,1] </td> <td>[30,3,1] </td> <td>[31,3,1] </td> <td>[32,3,1] </td> <td>[[33,3,1]] </td> <td>[34,3,1] </td></tr> <tr style="text-align:center;"> <th><a href="/wiki/Group_order" class="mw-redirect" title="Group order">Order</a> </th> <td>48 </td> <td>720 </td> <td>23,040 </td> <td>2,903,040 </td> <td colspan="2">∞ </td></tr> <tr style="text-align:center;"> <th>Graph </th> <td> </td> <td><a href="/wiki/File:5-simplex_t0.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/5-simplex_t0.svg/80px-5-simplex_t0.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/5-simplex_t0.svg/120px-5-simplex_t0.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/5-simplex_t0.svg/160px-5-simplex_t0.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a> </td> <td><a href="/wiki/File:Demihexeract_ortho_petrie.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/84/Demihexeract_ortho_petrie.svg/80px-Demihexeract_ortho_petrie.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/84/Demihexeract_ortho_petrie.svg/120px-Demihexeract_ortho_petrie.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/84/Demihexeract_ortho_petrie.svg/160px-Demihexeract_ortho_petrie.svg.png 2x" data-file-width="800" data-file-height="800" /></a> </td> <td><a href="/wiki/File:Up2_1_32_t0_E7.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Up2_1_32_t0_E7.svg/80px-Up2_1_32_t0_E7.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Up2_1_32_t0_E7.svg/120px-Up2_1_32_t0_E7.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/66/Up2_1_32_t0_E7.svg/160px-Up2_1_32_t0_E7.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> </td> <td>- </td> <td>- </td></tr> <tr style="text-align:center;"> <th>Name </th> <td><a href="/wiki/Dihedron" title="Dihedron">13,-1</a> </td> <td><a href="/wiki/5-simplex" title="5-simplex">130</a> </td> <td><a href="/wiki/6-demicube" title="6-demicube">131</a> </td> <td><a class="mw-selflink selflink">132</a> </td> <td><a href="/wiki/1_33_honeycomb" title="1 33 honeycomb">133</a> </td> <td><a href="/w/index.php?title=1_43_honeycomb&action=edit&redlink=1" class="new" title="1 43 honeycomb (page does not exist)">134</a> </td></tr></tbody></table> <table class="wikitable mw-collapsible mw-collapsed"> <tbody><tr> <th colspan="12"><a href="/wiki/Uniform_1_k2_polytope" title="Uniform 1 k2 polytope">1k2 figures</a> in n dimensions </th></tr> <tr> <th>Space </th> <th colspan="6">Finite </th> <th>Euclidean </th> <th>Hyperbolic </th></tr> <tr> <th>n </th> <th><a href="/wiki/Three-dimensional_space" title="Three-dimensional space">3</a> </th> <th><a href="/wiki/Four-dimensional_space" title="Four-dimensional space">4</a> </th> <th><a href="/wiki/Five-dimensional_space" title="Five-dimensional space">5</a> </th> <th><a href="/wiki/Six-dimensional_space" title="Six-dimensional space">6</a> </th> <th><a href="/wiki/Seven-dimensional_space" title="Seven-dimensional space">7</a> </th> <th><a href="/wiki/Eight-dimensional_space" title="Eight-dimensional space">8</a> </th> <th><a href="/wiki/Nine-dimensional_space" class="mw-redirect" title="Nine-dimensional space">9</a> </th> <th><a href="/wiki/Ten-dimensional_space" class="mw-redirect" title="Ten-dimensional space">10</a> </th></tr> <tr style="text-align:center;"> <th><a href="/wiki/Coxeter_group" title="Coxeter group">Coxeter group</a> </th> <td>E3=A2A1 </td> <td>E4=A4 </td> <td>E5=D5 </td> <td><a href="/wiki/E6_(mathematics)" title="E6 (mathematics)">E6</a> </td> <td><a href="/wiki/E7_(mathematics)" title="E7 (mathematics)">E7</a> </td> <td><a href="/wiki/E8_(mathematics)" title="E8 (mathematics)">E8</a> </td> <td>E9 = <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {E}}_{8}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {E}}_{8}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f7960ec54a7dac08a847e38ee3137a3e95a9044" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {E}}_{8}}"> = E8+ </td> <td>E10 = <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {T}}_{8}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>T</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {T}}_{8}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/897b8ae2da2454683a692ed6b588068316ee4816" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.828ex; height:2.843ex;" alt="{\displaystyle {\bar {T}}_{8}}"> = E8++ </td></tr> <tr style="text-align:center;"> <th><a href="/wiki/Coxeter%E2%80%93Dynkin_diagram" title="Coxeter–Dynkin diagram">Coxeter diagram</a> </th> <td><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/CDel_branch_01l.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td></tr> <tr style="text-align:center;"> <th><a href="/wiki/Coxeter_notation" title="Coxeter notation">Symmetry</a> (order) </th> <td>[3−1,2,1] </td> <td>[30,2,1] </td> <td>[31,2,1] </td> <td>[[32,2,1]] </td> <td>[33,2,1] </td> <td>[34,2,1] </td> <td>[35,2,1] </td> <td>[36,2,1] </td></tr> <tr style="text-align:center;"> <th><a href="/wiki/Group_order" class="mw-redirect" title="Group order">Order</a> </th> <td>12 </td> <td>120 </td> <td>1,920 </td> <td>103,680 </td> <td>2,903,040 </td> <td>696,729,600 </td> <td colspan="2">∞ </td></tr> <tr style="text-align:center;"> <th>Graph </th> <td><a href="/wiki/File:Trigonal_hosohedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Trigonal_hosohedron.png/80px-Trigonal_hosohedron.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Trigonal_hosohedron.png/120px-Trigonal_hosohedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Trigonal_hosohedron.png/160px-Trigonal_hosohedron.png 2x" data-file-width="620" data-file-height="622" /></a> </td> <td><a href="/wiki/File:4-simplex_t0.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/4-simplex_t0.svg/80px-4-simplex_t0.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/4-simplex_t0.svg/120px-4-simplex_t0.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b9/4-simplex_t0.svg/160px-4-simplex_t0.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a> </td> <td><a href="/wiki/File:Demipenteract_graph_ortho.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Demipenteract_graph_ortho.svg/80px-Demipenteract_graph_ortho.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Demipenteract_graph_ortho.svg/120px-Demipenteract_graph_ortho.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Demipenteract_graph_ortho.svg/160px-Demipenteract_graph_ortho.svg.png 2x" data-file-width="800" data-file-height="800" /></a> </td> <td><a href="/wiki/File:Up_1_22_t0_E6.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Up_1_22_t0_E6.svg/80px-Up_1_22_t0_E6.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Up_1_22_t0_E6.svg/120px-Up_1_22_t0_E6.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Up_1_22_t0_E6.svg/160px-Up_1_22_t0_E6.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> </td> <td><a href="/wiki/File:Up2_1_32_t0_E7.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Up2_1_32_t0_E7.svg/80px-Up2_1_32_t0_E7.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Up2_1_32_t0_E7.svg/120px-Up2_1_32_t0_E7.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/66/Up2_1_32_t0_E7.svg/160px-Up2_1_32_t0_E7.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> </td> <td><a href="/wiki/File:Gosset_1_42_polytope_petrie.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Gosset_1_42_polytope_petrie.svg/80px-Gosset_1_42_polytope_petrie.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Gosset_1_42_polytope_petrie.svg/120px-Gosset_1_42_polytope_petrie.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/32/Gosset_1_42_polytope_petrie.svg/160px-Gosset_1_42_polytope_petrie.svg.png 2x" data-file-width="800" data-file-height="800" /></a> </td> <td>- </td> <td>- </td></tr> <tr style="text-align:center;"> <th>Name </th> <td><a href="/wiki/Hosohedron" title="Hosohedron">1−1,2</a> </td> <td><a href="/wiki/5-cell" title="5-cell">102</a> </td> <td><a href="/wiki/Demipenteract" class="mw-redirect" title="Demipenteract">112</a> </td> <td><a href="/wiki/1_22_polytope" title="1 22 polytope">122</a> </td> <td><a class="mw-selflink selflink">132</a> </td> <td><a href="/wiki/1_42_polytope" title="1 42 polytope">142</a> </td> <td><a href="/wiki/1_52_honeycomb" title="1 52 honeycomb">152</a> </td> <td><a href="/wiki/1_62_honeycomb" class="mw-redirect" title="1 62 honeycomb">162</a> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Rectified_1_32_polytope">Rectified 1_32 polytope</h2>[<a href="/w/index.php?title=1_32_polytope&action=edit&section=6" title="Edit section: Rectified 1_32 polytope">edit</a>]</div> <table class="wikitable" align="right" style="margin-left:10px" width="280"> <tbody><tr> <th bgcolor="#e7dcc3" colspan="2">Rectified 132 </th></tr> <tr> <td bgcolor="#e7dcc3">Type</td> <td><a href="/wiki/Uniform_7-polytope" title="Uniform 7-polytope">Uniform 7-polytope</a> </td></tr> <tr> <td bgcolor="#e7dcc3"><a href="/wiki/Schl%C3%A4fli_symbol" title="Schläfli symbol">Schläfli symbol</a></td> <td>t1{3,33,2} </td></tr> <tr> <td bgcolor="#e7dcc3"><a href="/wiki/Coxeter_symbol" class="mw-redirect" title="Coxeter symbol">Coxeter symbol</a></td> <td>0321 </td></tr> <tr> <td bgcolor="#e7dcc3"><a href="/wiki/Coxeter-Dynkin_diagram" class="mw-redirect" title="Coxeter-Dynkin diagram">Coxeter-Dynkin diagram</a></td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/9/97/CDel_branch_10.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td></tr> <tr> <td bgcolor="#e7dcc3">6-faces</td> <td>758 </td></tr> <tr> <td bgcolor="#e7dcc3">5-faces</td> <td>12348 </td></tr> <tr> <td bgcolor="#e7dcc3">4-faces</td> <td>72072 </td></tr> <tr> <td bgcolor="#e7dcc3">Cells</td> <td>191520 </td></tr> <tr> <td bgcolor="#e7dcc3">Faces</td> <td>241920 </td></tr> <tr> <td bgcolor="#e7dcc3">Edges</td> <td>120960 </td></tr> <tr> <td bgcolor="#e7dcc3">Vertices</td> <td>10080 </td></tr> <tr> <td bgcolor="#e7dcc3"><a href="/wiki/Vertex_figure" title="Vertex figure">Vertex figure</a></td> <td>{3,3}×{3}×{} </td></tr> <tr> <td bgcolor="#e7dcc3"><a href="/wiki/Coxeter_group" title="Coxeter group">Coxeter group</a></td> <td><a href="/wiki/E7_(mathematics)" title="E7 (mathematics)">E7</a>, [33,2,1], order 2903040 </td></tr> <tr> <td bgcolor="#e7dcc3">Properties</td> <td><a href="/wiki/Convex_polytope" title="Convex polytope">convex</a> </td></tr></tbody></table> The rectified 132 (also called 0321) is a <a href="/wiki/Rectification_(geometry)" title="Rectification (geometry)">rectification</a> of the 132 polytope, creating new vertices on the center of edge of the 132. Its vertex figure is a duoprism prism, the product of a regular tetrahedra and triangle, doubled into a prism: {3,3}×{3}×{}. <div class="mw-heading mw-heading3"><h3 id="Alternate_names_2">Alternate names</h3>[<a href="/w/index.php?title=1_32_polytope&action=edit&section=7" title="Edit section: Alternate names">edit</a>]</div> <ul><li>Rectified pentacontihexa-hecatonicosihexa-exon for rectified 56-126 facetted polyexon (acronym rolin) (Jonathan Bowers)<a href="#cite_note-5">[5]</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Construction_2">Construction</h3>[<a href="/w/index.php?title=1_32_polytope&action=edit&section=8" title="Edit section: Construction">edit</a>]</div> It is created by a <a href="/wiki/Wythoff_construction" title="Wythoff construction">Wythoff construction</a> upon a set of 7 <a href="/wiki/Hyperplane" title="Hyperplane">hyperplane</a> mirrors in 7-dimensional space. These mirrors are represented by its <a href="/wiki/Coxeter-Dynkin_diagram" class="mw-redirect" title="Coxeter-Dynkin diagram">Coxeter-Dynkin diagram</a>, <img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/9/97/CDel_branch_10.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" />, and the ring represents the position of the active mirror(s). Removing the node on the end of the 3-length branch leaves the <a href="/wiki/Rectified_1_22_polytope" class="mw-redirect" title="Rectified 1 22 polytope">rectified 122</a> polytope, <img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> Removing the node on the end of the 2-length branch leaves the <a href="/wiki/Demihexeract" class="mw-redirect" title="Demihexeract">demihexeract</a>, 131, <img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/d/df/CDel_branch_01lr.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> Removing the node on the end of the 1-length branch leaves the <a href="/wiki/Birectified_6-simplex" class="mw-redirect" title="Birectified 6-simplex">birectified 6-simplex</a>, <img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/a/aa/CDel_nodea_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> The <a href="/wiki/Vertex_figure" title="Vertex figure">vertex figure</a> is determined by removing the ringed node and ringing the neighboring node. This makes the tetrahedron-triangle duoprism prism, {3,3}×{3}×{}, <img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/a/aa/CDel_nodea_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/a/aa/CDel_nodea_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/a/aa/CDel_nodea_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> Seen in a <a href="/wiki/Configuration_(polytope)" title="Configuration (polytope)">configuration matrix</a>, the element counts can be derived by mirror removal and ratios of <a href="/wiki/Coxeter_group#Properties" title="Coxeter group">Coxeter group</a> orders.<a href="#cite_note-6">[6]</a> <table class="wikitable" width="1700"> <tbody><tr> <th>E7</th> <th><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/9/97/CDel_branch_10.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></th> <th>k-face</th> <th>fk</th> <th>f0</th> <th>f1</th> <th colspan="3">f2</th> <th colspan="5">f3</th> <th colspan="6">f4</th> <th colspan="5">f5</th> <th colspan="3">f6</th> <th><a href="/wiki/Vertex_figure" title="Vertex figure">k-figures</a></th> <th>notes </th></tr> <tr align="right"> <td>A3A2A1</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/6/67/CDel_nodes_x0.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td>( ) </td> <th>f0 </th> <td bgcolor="#ffe0ff">10080</td> <td>24</td> <td>24</td> <td>12</td> <td>36</td> <td>8</td> <td>12</td> <td>36</td> <td>18</td> <td>24</td> <td>4</td> <td>12</td> <td>18</td> <td>24</td> <td>12</td> <td>6</td> <td>6</td> <td>8</td> <td>12</td> <td>6</td> <td>3</td> <td>4</td> <td>2</td> <td>3</td> <td>{3,3}x{3}x{ }</td> <td>E7/A3A2A1 = 72*8!/4!/3!/2 = 10080 </td></tr> <tr align="right"> <td>A2A1A1</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/7/79/CDel_nodes_1x.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td>{ } </td> <th>f1 </th> <td>2</td> <td bgcolor="#ffe0e0">120960</td> <td>2</td> <td>1</td> <td>3</td> <td>1</td> <td>2</td> <td>6</td> <td>3</td> <td>3</td> <td>1</td> <td>3</td> <td>6</td> <td>6</td> <td>3</td> <td>1</td> <td>3</td> <td>3</td> <td>6</td> <td>2</td> <td>1</td> <td>3</td> <td>1</td> <td>2</td> <td>( )v{3}v{ }</td> <td>E7/A2A1A1 = 72*8!/3!/2/2 = 120960 </td></tr> <tr align="right"> <td>A2A2</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/7/79/CDel_nodes_1x.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td rowspan="3"><a href="/wiki/Triangle" title="Triangle">01</a> </td> <th rowspan="3">f2 </th> <td>3</td> <td>3</td> <td bgcolor="#ffffe0">80640</td> <td bgcolor="#ffffe0">*</td> <td bgcolor="#ffffe0">*</td> <td>1</td> <td>1</td> <td>3</td> <td>0</td> <td>0</td> <td>1</td> <td>3</td> <td>3</td> <td>3</td> <td>0</td> <td>0</td> <td>3</td> <td>3</td> <td>3</td> <td>1</td> <td>0</td> <td>3</td> <td>1</td> <td>1</td> <td>{3}v( )v( )</td> <td>E7/A2A2 = 72*8!/3!/3! = 80640 </td></tr> <tr align="right"> <td>A2A2A1</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/9/97/CDel_branch_10.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td>3</td> <td>3</td> <td bgcolor="#ffffe0">*</td> <td bgcolor="#ffffe0">40320</td> <td bgcolor="#ffffe0">*</td> <td>0</td> <td>2</td> <td>0</td> <td>3</td> <td>0</td> <td>1</td> <td>0</td> <td>6</td> <td>0</td> <td>3</td> <td>0</td> <td>3</td> <td>0</td> <td>6</td> <td>0</td> <td>1</td> <td>3</td> <td>0</td> <td>2</td> <td>{3}v{ }</td> <td>E7/A2A2A1 = 72*8!/3!/3!/2 = 40320 </td></tr> <tr align="right"> <td>A2A1A1</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/7/79/CDel_nodes_1x.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td>3</td> <td>3</td> <td bgcolor="#ffffe0">*</td> <td bgcolor="#ffffe0">*</td> <td bgcolor="#ffffe0">120960</td> <td>0</td> <td>0</td> <td>2</td> <td>1</td> <td>2</td> <td>0</td> <td>1</td> <td>2</td> <td>4</td> <td>2</td> <td>1</td> <td>1</td> <td>2</td> <td>4</td> <td>2</td> <td>1</td> <td>2</td> <td>1</td> <td>2</td> <td>{ }v{ }v( )</td> <td>E7/A2A1A1 = 72*8!/3!/2/2 = 120960 </td></tr> <tr align="right"> <td rowspan="2">A3A2</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/7/79/CDel_nodes_1x.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td><a href="/wiki/Tetrahedron" title="Tetrahedron">02</a> </td> <th rowspan="5">f3 </th> <td>4</td> <td>6</td> <td>4</td> <td>0</td> <td>0</td> <td bgcolor="#e0ffe0">20160</td> <td bgcolor="#e0ffe0">*</td> <td bgcolor="#e0ffe0">*</td> <td bgcolor="#e0ffe0">*</td> <td bgcolor="#e0ffe0">*</td> <td>1</td> <td>3</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td>3</td> <td>3</td> <td>0</td> <td>0</td> <td>0</td> <td>3</td> <td>1</td> <td>0</td> <td rowspan="2"><a href="/wiki/Triangular_pyramid" class="mw-redirect" title="Triangular pyramid">{3}v( )</a></td> <td rowspan="2">E7/A3A2 = 72*8!/4!/3! = 20160 </td></tr> <tr align="right"> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/9/97/CDel_branch_10.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td rowspan="3"><a href="/wiki/Octahedron" title="Octahedron">011</a> </td> <td>6</td> <td>12</td> <td>4</td> <td>4</td> <td>0</td> <td bgcolor="#e0ffe0">*</td> <td bgcolor="#e0ffe0">20160</td> <td bgcolor="#e0ffe0">*</td> <td bgcolor="#e0ffe0">*</td> <td bgcolor="#e0ffe0">*</td> <td>1</td> <td>0</td> <td>3</td> <td>0</td> <td>0</td> <td>0</td> <td>3</td> <td>0</td> <td>3</td> <td>0</td> <td>0</td> <td>3</td> <td>0</td> <td>1 </td></tr> <tr align="right"> <td>A3A1</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/7/79/CDel_nodes_1x.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td>6</td> <td>12</td> <td>4</td> <td>0</td> <td>4</td> <td bgcolor="#e0ffe0">*</td> <td bgcolor="#e0ffe0">*</td> <td bgcolor="#e0ffe0">60480</td> <td bgcolor="#e0ffe0">*</td> <td bgcolor="#e0ffe0">*</td> <td>0</td> <td>1</td> <td>1</td> <td>2</td> <td>0</td> <td>0</td> <td>1</td> <td>2</td> <td>2</td> <td>1</td> <td>0</td> <td>2</td> <td>1</td> <td>1</td> <td><a href="/wiki/Mirrored_sphenoid" class="mw-redirect" title="Mirrored sphenoid">Sphenoid</a></td> <td>E7/A3A1 = 72*8!/4!/2 = 60480 </td></tr> <tr align="right"> <td>A3A1A1</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/9/97/CDel_branch_10.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td>6</td> <td>12</td> <td>0</td> <td>4</td> <td>4</td> <td bgcolor="#e0ffe0">*</td> <td bgcolor="#e0ffe0">*</td> <td bgcolor="#e0ffe0">*</td> <td bgcolor="#e0ffe0">30240</td> <td bgcolor="#e0ffe0">*</td> <td>0</td> <td>0</td> <td>2</td> <td>0</td> <td>2</td> <td>0</td> <td>1</td> <td>0</td> <td>4</td> <td>0</td> <td>1</td> <td>2</td> <td>0</td> <td>2</td> <td><a href="/wiki/Digonal_disphenoid" class="mw-redirect" title="Digonal disphenoid">{ }v{ }</a></td> <td>E7/A3A1A1 = 72*8!/4!/2/2 = 30240 </td></tr> <tr align="right"> <td>A3A1</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/7/79/CDel_nodes_1x.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td>02 </td> <td>4</td> <td>6</td> <td>0</td> <td>0</td> <td>4</td> <td bgcolor="#e0ffe0">*</td> <td bgcolor="#e0ffe0">*</td> <td bgcolor="#e0ffe0">*</td> <td bgcolor="#e0ffe0">*</td> <td bgcolor="#e0ffe0">60480</td> <td>0</td> <td>0</td> <td>0</td> <td>2</td> <td>1</td> <td>1</td> <td>0</td> <td>1</td> <td>2</td> <td>2</td> <td>1</td> <td>1</td> <td>1</td> <td>2</td> <td>Sphenoid</td> <td>E7/A3A1 = 72*8!/4!/2 = 60480 </td></tr> <tr align="right"> <td>A4A2</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/9/97/CDel_branch_10.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td rowspan="2"><a href="/wiki/Rectified_5-cell" title="Rectified 5-cell">021</a> </td> <th rowspan="6">f4 </th> <td>10</td> <td>30</td> <td>20</td> <td>10</td> <td>0</td> <td>5</td> <td>5</td> <td>0</td> <td>0</td> <td>0</td> <td bgcolor="#e0ffff">4032</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td>3</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td>3</td> <td>0</td> <td>0</td> <td><a href="/wiki/Equilateral_triangle" title="Equilateral triangle">{3}</a></td> <td>E7/A4A2 = 72*8!/5!/3! = 4032 </td></tr> <tr align="right"> <td>A4A1</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/7/79/CDel_nodes_1x.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td>10</td> <td>30</td> <td>20</td> <td>0</td> <td>10</td> <td>5</td> <td>0</td> <td>5</td> <td>0</td> <td>0</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">12096</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td>1</td> <td>2</td> <td>0</td> <td>0</td> <td>0</td> <td>2</td> <td>1</td> <td>0</td> <td rowspan="2"><a href="/wiki/Isosceles_triangle" title="Isosceles triangle">{ }v()</a></td> <td>E7/A4A1 = 72*8!/5!/2 = 12096 </td></tr> <tr align="right"> <td>D4A1</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/9/97/CDel_branch_10.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td><a href="/wiki/16-cell" title="16-cell">0111</a> </td> <td>24</td> <td>96</td> <td>32</td> <td>32</td> <td>32</td> <td>0</td> <td>8</td> <td>8</td> <td>8</td> <td>0</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">7560</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td>1</td> <td>0</td> <td>2</td> <td>0</td> <td>0</td> <td>2</td> <td>0</td> <td>1</td> <td>E7/D4A1 = 72*8!/8/4!/2 = 7560 </td></tr> <tr align="right"> <td>A4</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/7/79/CDel_nodes_1x.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td rowspan="2">021 </td> <td>10</td> <td>30</td> <td>10</td> <td>0</td> <td>20</td> <td>0</td> <td>0</td> <td>5</td> <td>0</td> <td>5</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">24192</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td>0</td> <td>1</td> <td>1</td> <td>1</td> <td>0</td> <td>1</td> <td>1</td> <td>1</td> <td><a href="/wiki/Scalene_triangle" class="mw-redirect" title="Scalene triangle">( )v( )v( )</a></td> <td>E7/A4 = 72*8!/5! = 34192 </td></tr> <tr align="right"> <td rowspan="2">A4A1</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/9/97/CDel_branch_10.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td>10</td> <td>30</td> <td>0</td> <td>10</td> <td>20</td> <td>0</td> <td>0</td> <td>0</td> <td>5</td> <td>5</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">12096</td> <td bgcolor="#e0ffff">*</td> <td>0</td> <td>0</td> <td>2</td> <td>0</td> <td>1</td> <td>1</td> <td>0</td> <td>2</td> <td rowspan="2"><a href="/wiki/Isosceles_triangle" title="Isosceles triangle">{ }v()</a></td> <td rowspan="2">E7/A4A1 = 72*8!/5!/2 = 12096 </td></tr> <tr align="right"> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/7/79/CDel_nodes_1x.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td>03 </td> <td>5</td> <td>10</td> <td>0</td> <td>0</td> <td>10</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td>5</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">*</td> <td bgcolor="#e0ffff">12096</td> <td>0</td> <td>0</td> <td>0</td> <td>2</td> <td>1</td> <td>0</td> <td>1</td> <td>2 </td></tr> <tr align="right"> <td>D5A1</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/9/97/CDel_branch_10.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td><a href="/wiki/Rectified_5-demicube" class="mw-redirect" title="Rectified 5-demicube">0211</a> </td> <th rowspan="5">f5 </th> <td>80</td> <td>480</td> <td>320</td> <td>160</td> <td>160</td> <td>80</td> <td>80</td> <td>80</td> <td>40</td> <td>0</td> <td>16</td> <td>16</td> <td>10</td> <td>0</td> <td>0</td> <td>0</td> <td bgcolor="#e0e0ff">756</td> <td bgcolor="#e0e0ff">*</td> <td bgcolor="#e0e0ff">*</td> <td bgcolor="#e0e0ff">*</td> <td bgcolor="#e0e0ff">*</td> <td>2</td> <td>0</td> <td>0</td> <td rowspan="5">{ }</td> <td>E7/D5A1 = 72*8!/16/5!/2 = 756 </td></tr> <tr align="right"> <td>A5</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/7/79/CDel_nodes_1x.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td><a href="/wiki/Birectified_5-simplex" class="mw-redirect" title="Birectified 5-simplex">022</a> </td> <td>20</td> <td>90</td> <td>60</td> <td>0</td> <td>60</td> <td>15</td> <td>0</td> <td>30</td> <td>0</td> <td>15</td> <td>0</td> <td>6</td> <td>0</td> <td>6</td> <td>0</td> <td>0</td> <td bgcolor="#e0e0ff">*</td> <td bgcolor="#e0e0ff">4032</td> <td bgcolor="#e0e0ff">*</td> <td bgcolor="#e0e0ff">*</td> <td bgcolor="#e0e0ff">*</td> <td>1</td> <td>1</td> <td>0</td> <td>E7/A5 = 72*8!/6! = 4032 </td></tr> <tr align="right"> <td>D5</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/9/97/CDel_branch_10.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td>0211 </td> <td>80</td> <td>480</td> <td>160</td> <td>160</td> <td>320</td> <td>0</td> <td>40</td> <td>80</td> <td>80</td> <td>80</td> <td>0</td> <td>0</td> <td>10</td> <td>16</td> <td>16</td> <td>0</td> <td bgcolor="#e0e0ff">*</td> <td bgcolor="#e0e0ff">*</td> <td bgcolor="#e0e0ff">1512</td> <td bgcolor="#e0e0ff">*</td> <td bgcolor="#e0e0ff">*</td> <td>1</td> <td>0</td> <td>1</td> <td>E7/D5 = 72*8!/16/5! = 1512 </td></tr> <tr align="right"> <td>A5</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/7/79/CDel_nodes_1x.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td rowspan="2">031 </td> <td>15</td> <td>60</td> <td>20</td> <td>0</td> <td>60</td> <td>0</td> <td>0</td> <td>15</td> <td>0</td> <td>30</td> <td>0</td> <td>0</td> <td>0</td> <td>6</td> <td>0</td> <td>6</td> <td bgcolor="#e0e0ff">*</td> <td bgcolor="#e0e0ff">*</td> <td bgcolor="#e0e0ff">*</td> <td bgcolor="#e0e0ff">4032</td> <td bgcolor="#e0e0ff">*</td> <td>0</td> <td>1</td> <td>1</td> <td>E7/A5 = 72*8!/6! = 4032 </td></tr> <tr align="right"> <td>A5A1</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/9/97/CDel_branch_10.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td>15</td> <td>60</td> <td>0</td> <td>20</td> <td>60</td> <td>0</td> <td>0</td> <td>0</td> <td>15</td> <td>30</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td>6</td> <td>6</td> <td bgcolor="#e0e0ff">*</td> <td bgcolor="#e0e0ff">*</td> <td bgcolor="#e0e0ff">*</td> <td bgcolor="#e0e0ff">*</td> <td bgcolor="#e0e0ff">2016</td> <td>0</td> <td>0</td> <td>2</td> <td>E7/A5A1 = 72*8!/6!/2 = 2016 </td></tr> <tr align="right"> <td>E6</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/9/97/CDel_branch_10.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td><a href="/wiki/Rectified_1_22_polytope" class="mw-redirect" title="Rectified 1 22 polytope">0221</a> </td> <th rowspan="3">f6 </th> <td>720</td> <td>6480</td> <td>4320</td> <td>2160</td> <td>4320</td> <td>1080</td> <td>1080</td> <td>2160</td> <td>1080</td> <td>1080</td> <td>216</td> <td>432</td> <td>270</td> <td>432</td> <td>216</td> <td>0</td> <td>27</td> <td>72</td> <td>27</td> <td>0</td> <td>0</td> <td bgcolor="#ffe0ff">56</td> <td bgcolor="#ffe0ff">*</td> <td bgcolor="#ffe0ff">*</td> <td rowspan="3">( )</td> <td>E7/E6 = 72*8!/72/6! = 56 </td></tr> <tr align="right"> <td>A6</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/7/79/CDel_nodes_1x.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td><a href="/wiki/Birectified_6-simplex" class="mw-redirect" title="Birectified 6-simplex">032</a> </td> <td>35</td> <td>210</td> <td>140</td> <td>0</td> <td>210</td> <td>35</td> <td>0</td> <td>105</td> <td>0</td> <td>105</td> <td>0</td> <td>21</td> <td>0</td> <td>42</td> <td>0</td> <td>21</td> <td>0</td> <td>7</td> <td>0</td> <td>7</td> <td>0</td> <td bgcolor="#ffe0ff">*</td> <td bgcolor="#ffe0ff">576</td> <td bgcolor="#ffe0ff">*</td> <td>E7/A6 = 72*8!/7! = 576 </td></tr> <tr align="right"> <td>D6</td> <td><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/9/97/CDel_branch_10.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_3a.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/CDel_nodea.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/85/CDel_nodea_x.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></td> <td><a href="/wiki/Rectified_6-demicube" class="mw-redirect" title="Rectified 6-demicube">0311</a> </td> <td>240</td> <td>1920</td> <td>640</td> <td>640</td> <td>1920</td> <td>0</td> <td>160</td> <td>480</td> <td>480</td> <td>960</td> <td>0</td> <td>0</td> <td>60</td> <td>192</td> <td>192</td> <td>192</td> <td>0</td> <td>0</td> <td>12</td> <td>32</td> <td>32</td> <td bgcolor="#ffe0ff">*</td> <td bgcolor="#ffe0ff">*</td> <td bgcolor="#ffe0ff">126</td> <td>E7/D6 = 72*8!/32/6! = 126 </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Images_2">Images</h3>[<a href="/w/index.php?title=1_32_polytope&action=edit&section=9" title="Edit section: Images">edit</a>]</div> <table class="wikitable" width="600"> <caption><a href="/wiki/Coxeter_plane" class="mw-redirect" title="Coxeter plane">Coxeter plane</a> projections </caption> <tbody><tr> <th>E7 </th> <th>E6 / F4 </th> <th>B7 / A6 </th></tr> <tr valign="top" align="center"> <td><a href="/wiki/File:Up2_1_32_t1_E7.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Up2_1_32_t1_E7.svg/200px-Up2_1_32_t1_E7.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Up2_1_32_t1_E7.svg/300px-Up2_1_32_t1_E7.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Up2_1_32_t1_E7.svg/400px-Up2_1_32_t1_E7.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> [18] </td> <td><a href="/wiki/File:Up2_1_32_t1_E6.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Up2_1_32_t1_E6.svg/200px-Up2_1_32_t1_E6.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Up2_1_32_t1_E6.svg/300px-Up2_1_32_t1_E6.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/90/Up2_1_32_t1_E6.svg/400px-Up2_1_32_t1_E6.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> [12] </td> <td><a href="/wiki/File:Up2_1_32_t1_A6.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Up2_1_32_t1_A6.svg/200px-Up2_1_32_t1_A6.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Up2_1_32_t1_A6.svg/300px-Up2_1_32_t1_A6.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Up2_1_32_t1_A6.svg/400px-Up2_1_32_t1_A6.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> [14] </td></tr> <tr> <th>A5 </th> <th>D7 / B6 </th> <th>D6 / B5 </th></tr> <tr valign="top" align="center"> <td><a href="/wiki/File:Up2_1_32_t1_A5.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Up2_1_32_t1_A5.svg/200px-Up2_1_32_t1_A5.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Up2_1_32_t1_A5.svg/300px-Up2_1_32_t1_A5.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Up2_1_32_t1_A5.svg/400px-Up2_1_32_t1_A5.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> [6] </td> <td><a href="/wiki/File:Up2_1_32_t1_D7.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Up2_1_32_t1_D7.svg/200px-Up2_1_32_t1_D7.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Up2_1_32_t1_D7.svg/300px-Up2_1_32_t1_D7.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Up2_1_32_t1_D7.svg/400px-Up2_1_32_t1_D7.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> [12/2] </td> <td><a href="/wiki/File:Up2_1_32_t1_D6.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Up2_1_32_t1_D6.svg/200px-Up2_1_32_t1_D6.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Up2_1_32_t1_D6.svg/300px-Up2_1_32_t1_D6.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/Up2_1_32_t1_D6.svg/400px-Up2_1_32_t1_D6.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> [10] </td></tr> <tr> <th>D5 / B4 / A4 </th> <th>D4 / B3 / A2 / G2 </th> <th>D3 / B2 / A3 </th></tr> <tr valign="top" align="center"> <td><a href="/wiki/File:Up2_1_32_t1_D5.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Up2_1_32_t1_D5.svg/200px-Up2_1_32_t1_D5.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Up2_1_32_t1_D5.svg/300px-Up2_1_32_t1_D5.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/15/Up2_1_32_t1_D5.svg/400px-Up2_1_32_t1_D5.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> [8] </td> <td><a href="/wiki/File:Up2_1_32_t1_D4.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Up2_1_32_t1_D4.svg/200px-Up2_1_32_t1_D4.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Up2_1_32_t1_D4.svg/300px-Up2_1_32_t1_D4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Up2_1_32_t1_D4.svg/400px-Up2_1_32_t1_D4.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> [6] </td> <td><a href="/wiki/File:Up2_1_32_t1_D3.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Up2_1_32_t1_D3.svg/200px-Up2_1_32_t1_D3.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Up2_1_32_t1_D3.svg/300px-Up2_1_32_t1_D3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Up2_1_32_t1_D3.svg/400px-Up2_1_32_t1_D3.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a> [4] </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2>[<a href="/w/index.php?title=1_32_polytope&action=edit&section=10" title="Edit section: See also">edit</a>]</div> <ul><li><a href="/wiki/List_of_E7_polytopes" class="mw-redirect" title="List of E7 polytopes">List of E7 polytopes</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2>[<a href="/w/index.php?title=1_32_polytope&action=edit&section=11" title="Edit section: Notes">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">^</a> <a rel="nofollow" class="external text" href="http://home.digital.net/~pervin/publications/vermont.html">The Voronoi Cells of the E6* and E7* Lattices</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160130193811/http://home.digital.net/~pervin/publications/vermont.html">Archived</a> 2016-01-30 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, Edward Pervin </li> <li id="cite_note-2"><a href="#cite_ref-2">^</a> Elte, 1912 </li> <li id="cite_note-3"><a href="#cite_ref-3">^</a> Klitzing, (o3o3o3x *c3o3o3o - lin) </li> <li id="cite_note-4"><a href="#cite_ref-4">^</a> Coxeter, Regular Polytopes, 11.8 Gossett figures in six, seven, and eight dimensions, p. 202-203 </li> <li id="cite_note-5"><a href="#cite_ref-5">^</a> Klitzing, (o3o3x3o *c3o3o3o - rolin) </li> <li id="cite_note-6"><a href="#cite_ref-6">^</a> Coxeter, Regular Polytopes, 11.8 Gossett figures in six, seven, and eight dimensions, p. 202-203 </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2>[<a href="/w/index.php?title=1_32_polytope&action=edit&section=12" title="Edit section: References">edit</a>]</div> <ul><li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFElte1912" class="citation cs2">Elte, E. L. (1912), The Semiregular Polytopes of the Hyperspaces, Groningen: University of Groningen</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Semiregular+Polytopes+of+the+Hyperspaces&rft.place=Groningen&rft.pub=University+of+Groningen&rft.date=1912&rft.aulast=Elte&rft.aufirst=E.+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3A1+32+polytope" class="Z3988"></li> <li><a href="/wiki/Harold_Scott_MacDonald_Coxeter" title="Harold Scott MacDonald Coxeter">H. S. M. Coxeter</a>, Regular Polytopes, 3rd Edition, Dover New York, 1973</li> <li>Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-01003-6" title="Special:BookSources/978-0-471-01003-6">978-0-471-01003-6</a> <a rel="nofollow" class="external autonumber" href="http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html">[1]</a> <ul><li>(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]</li></ul></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKlitzing" class="citation web cs1">Klitzing, Richard. <a rel="nofollow" class="external text" href="https://bendwavy.org/klitzing/dimensions/polyexa.htm">"7D uniform polytopes (polyexa)"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=7D+uniform+polytopes+%28polyexa%29&rft.aulast=Klitzing&rft.aufirst=Richard&rft_id=https%3A%2F%2Fbendwavy.org%2Fklitzing%2Fdimensions%2Fpolyexa.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3A1+32+polytope" class="Z3988"> o3o3o3x *c3o3o3o - lin, o3o3x3o *c3o3o3o - rolin</li></ul> <table class="wikitable mw-collapsible"> <tbody><tr> <th colspan="13" style="background:lightsteelblue;"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist 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abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-collapse navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Polytopes" title="Template:Polytopes"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Polytopes" title="Template talk:Polytopes"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Polytopes" title="Special:EditPage/Template:Polytopes"><abbr title="Edit this template">e</abbr></a></li></ul></div><div class="navbar-ct-mini">Fundamental convex <a href="/wiki/Regular_polytope" title="Regular polytope">regular</a> and <a href="/wiki/Uniform_polytope" title="Uniform polytope">uniform polytopes</a> in dimensions 2–10</div> </th></tr> <tr style="text-align:center;"> <th style="background:gainsboro;"><a href="/wiki/Coxeter_group#Finite_Coxeter_groups" title="Coxeter group">Family</a> </th> <td style="background:gainsboro;"><a href="/wiki/Simple_Lie_group#A_series" title="Simple Lie group">An</a> </td> <td style="background:gainsboro;"><a href="/wiki/Simple_Lie_group#B_series" title="Simple Lie group">Bn</a> </td> <td style="background:gainsboro;">I2(p) / <a href="/wiki/Simple_Lie_group#D_series" title="Simple Lie group">Dn</a> </td> <td style="background:gainsboro;"><a href="/wiki/E6_(mathematics)" title="E6 (mathematics)">E6</a> / <a href="/wiki/E7_(mathematics)" title="E7 (mathematics)">E7</a> / <a href="/wiki/E8_(mathematics)" title="E8 (mathematics)">E8</a> / <a href="/wiki/F4_(mathematics)" title="F4 (mathematics)">F4</a> / <a href="/wiki/G2_(mathematics)" title="G2 (mathematics)">G2</a> </td> <td style="background:gainsboro;"><a href="/wiki/H4_(mathematics)" class="mw-redirect" title="H4 (mathematics)">Hn</a> </td></tr> <tr style="text-align:center;"> <th style="background:gainsboro;"><a href="/wiki/Regular_polygon" title="Regular polygon">Regular polygon</a> </th> <td><a href="/wiki/Equilateral_triangle" title="Equilateral triangle">Triangle</a> </td> <td><a href="/wiki/Square" title="Square">Square</a> </td> <td style="background:#f0f0e0;"><a href="/wiki/Regular_polygon" title="Regular polygon">p-gon</a> </td> <td style="background:#e0e0f0;"><a href="/wiki/Hexagon" title="Hexagon">Hexagon</a> </td> <td><a href="/wiki/Pentagon" title="Pentagon">Pentagon</a> </td></tr> <tr style="text-align:center;"> <th style="background:gainsboro;"><a href="/wiki/Uniform_polyhedron" title="Uniform polyhedron">Uniform polyhedron</a> </th> <td style="background:whitesmoke;"><a href="/wiki/Tetrahedron" title="Tetrahedron">Tetrahedron</a> </td> <td style="background:whitesmoke;"><a href="/wiki/Octahedron" title="Octahedron">Octahedron</a> • <a href="/wiki/Cube" title="Cube">Cube</a> </td> <td style="background:whitesmoke;"><a href="/wiki/Tetrahedron" title="Tetrahedron">Demicube</a> </td> <td style="background:whitesmoke;"> </td> <td style="background:whitesmoke;"><a href="/wiki/Regular_dodecahedron" title="Regular dodecahedron">Dodecahedron</a> • <a href="/wiki/Regular_icosahedron" title="Regular icosahedron">Icosahedron</a> </td></tr> <tr style="text-align:center;"> <th style="background:gainsboro;"><a href="/wiki/Uniform_polychoron" class="mw-redirect" title="Uniform polychoron">Uniform polychoron</a> </th> <td><a href="/wiki/5-cell" title="5-cell">Pentachoron</a> </td> <td><a href="/wiki/16-cell" title="16-cell">16-cell</a> • <a href="/wiki/Tesseract" title="Tesseract">Tesseract</a> </td> <td><a href="/wiki/16-cell" title="16-cell">Demitesseract</a> </td> <td style="background:#e0f0e0;"><a href="/wiki/24-cell" title="24-cell">24-cell</a> </td> <td><a href="/wiki/120-cell" title="120-cell">120-cell</a> • <a href="/wiki/600-cell" title="600-cell">600-cell</a> </td></tr> <tr style="text-align:center;"> <th style="background:gainsboro;"><a href="/wiki/Uniform_5-polytope" title="Uniform 5-polytope">Uniform 5-polytope</a> </th> <td style="background:whitesmoke;"><a href="/wiki/5-simplex" title="5-simplex">5-simplex</a> </td> <td style="background:whitesmoke;"><a href="/wiki/5-orthoplex" title="5-orthoplex">5-orthoplex</a> • <a href="/wiki/5-cube" title="5-cube">5-cube</a> </td> <td style="background:whitesmoke;"><a href="/wiki/5-demicube" title="5-demicube">5-demicube</a> </td> <td style="background:whitesmoke;"> </td> <td style="background:whitesmoke;"> </td></tr> <tr style="text-align:center;"> <th style="background:gainsboro;"><a href="/wiki/Uniform_6-polytope" title="Uniform 6-polytope">Uniform 6-polytope</a> </th> <td><a href="/wiki/6-simplex" title="6-simplex">6-simplex</a> </td> <td><a href="/wiki/6-orthoplex" title="6-orthoplex">6-orthoplex</a> • <a href="/wiki/6-cube" title="6-cube">6-cube</a> </td> <td><a href="/wiki/6-demicube" title="6-demicube">6-demicube</a> </td> <td style="background:#f0e0e0;"><a href="/wiki/1_22_polytope" title="1 22 polytope">122</a> • <a href="/wiki/2_21_polytope" title="2 21 polytope">221</a> </td> <td> </td></tr> <tr style="text-align:center;"> <th style="background:gainsboro;"><a href="/wiki/Uniform_7-polytope" title="Uniform 7-polytope">Uniform 7-polytope</a> </th> <td style="background:whitesmoke;"><a href="/wiki/7-simplex" title="7-simplex">7-simplex</a> </td> <td style="background:whitesmoke;"><a href="/wiki/7-orthoplex" title="7-orthoplex">7-orthoplex</a> • <a href="/wiki/7-cube" title="7-cube">7-cube</a> </td> <td style="background:whitesmoke;"><a href="/wiki/7-demicube" title="7-demicube">7-demicube</a> </td> <td style="background:#f0e0e0;"><a class="mw-selflink selflink">132</a> • <a href="/wiki/2_31_polytope" title="2 31 polytope">231</a> • <a href="/wiki/3_21_polytope" title="3 21 polytope">321</a> </td> <td style="background:whitesmoke;"> </td></tr> <tr style="text-align:center;"> <th style="background:gainsboro;"><a href="/wiki/Uniform_8-polytope" title="Uniform 8-polytope">Uniform 8-polytope</a> </th> <td><a href="/wiki/8-simplex" title="8-simplex">8-simplex</a> </td> <td><a href="/wiki/8-orthoplex" title="8-orthoplex">8-orthoplex</a> • <a href="/wiki/8-cube" title="8-cube">8-cube</a> </td> <td><a href="/wiki/8-demicube" title="8-demicube">8-demicube</a> </td> <td style="background:#f0e0e0;"><a href="/wiki/1_42_polytope" title="1 42 polytope">142</a> • <a href="/wiki/2_41_polytope" title="2 41 polytope">241</a> • <a href="/wiki/4_21_polytope" title="4 21 polytope">421</a> </td> <td> </td></tr> <tr style="text-align:center;"> <th style="background:gainsboro;"><a href="/wiki/Uniform_9-polytope" title="Uniform 9-polytope">Uniform 9-polytope</a> </th> <td style="background:whitesmoke;"><a href="/wiki/9-simplex" title="9-simplex">9-simplex</a> </td> <td style="background:whitesmoke;"><a href="/wiki/9-orthoplex" title="9-orthoplex">9-orthoplex</a> • <a href="/wiki/9-cube" title="9-cube">9-cube</a> </td> <td style="background:whitesmoke;"><a href="/wiki/9-demicube" title="9-demicube">9-demicube</a> </td> <td style="background:whitesmoke;"> </td> <td style="background:whitesmoke;"> </td></tr> <tr style="text-align:center;"> <th style="background:gainsboro;"><a href="/wiki/Uniform_10-polytope" title="Uniform 10-polytope">Uniform 10-polytope</a> </th> <td><a href="/wiki/10-simplex" title="10-simplex">10-simplex</a> </td> <td><a href="/wiki/10-orthoplex" title="10-orthoplex">10-orthoplex</a> • <a href="/wiki/10-cube" title="10-cube">10-cube</a> </td> <td><a href="/wiki/10-demicube" title="10-demicube">10-demicube</a> </td> <td> </td> <td> </td></tr> <tr style="text-align:center;"> <th style="background:gainsboro;">Uniform n-<a href="/wiki/Polytope" title="Polytope">polytope</a> </th> <td style="background:whitesmoke;">n-<a href="/wiki/Simplex" title="Simplex">simplex</a> </td> <td style="background:whitesmoke;">n-<a href="/wiki/Cross-polytope" title="Cross-polytope">orthoplex</a> • n-<a href="/wiki/Hypercube" title="Hypercube">cube</a> </td> <td style="background:whitesmoke;">n-<a href="/wiki/Demihypercube" title="Demihypercube">demicube</a> </td> <td style="background:#f0e0e0;"><a href="/wiki/Uniform_1_k2_polytope" title="Uniform 1 k2 polytope">1k2</a> • <a href="/wiki/Uniform_2_k1_polytope" title="Uniform 2 k1 polytope">2k1</a> • <a href="/wiki/Uniform_k_21_polytope" title="Uniform k 21 polytope">k21</a> </td> <td style="background:whitesmoke;">n-<a href="/wiki/Pentagonal_polytope" title="Pentagonal polytope">pentagonal polytope</a> </td></tr> <tr style="text-align:center;"> <th colspan="13" style="background:gainsboro;">Topics: <a href="/wiki/Polytope_families" title="Polytope families">Polytope families</a> • <a href="/wiki/Regular_polytope" title="Regular polytope">Regular polytope</a> • <a href="/wiki/List_of_regular_polytopes_and_compounds" class="mw-redirect" title="List of regular polytopes and compounds">List of regular polytopes and compounds</a> </th></tr></tbody></table>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=1_32_polytope&oldid=1218108477">https://en.wikipedia.org/w/index.php?title=1_32_polytope&oldid=1218108477</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Category</a>: <ul><li><a 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