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class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Images"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Images</span> </div> </a> <ul id="toc-Images-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Birectified_5-cube" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Birectified_5-cube"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Birectified 5-cube</span> </div> </a> <button aria-controls="toc-Birectified_5-cube-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Birectified 5-cube subsection</span> </button> <ul id="toc-Birectified_5-cube-sublist" class="vector-toc-list"> <li id="toc-Alternate_names_2" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" 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href="#Related_polytopes"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Related polytopes</span> </div> </a> <ul id="toc-Related_polytopes-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Related_polytopes_2" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Related_polytopes_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Related polytopes</span> </div> </a> <ul id="toc-Related_polytopes_2-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"> <span class="vector-toc-numb">4</span> <span>Notes</span> </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"> <span class="vector-toc-numb">5</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" 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title="Wikipedia:When to cite">introducing</a> more precise citations.</span> <span class="date-container"><i>(<span class="date">October 2022</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <table class="wikitable" align="right" style="margin-left:1em;"> <tbody><tr align="center"> <td><span typeof="mw:File"><a href="/wiki/File:5-cube_t0.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/5-cube_t0.svg/100px-5-cube_t0.svg.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/5-cube_t0.svg/150px-5-cube_t0.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b1/5-cube_t0.svg/200px-5-cube_t0.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/5-cube" title="5-cube">5-cube</a><br /><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:5-cube_t1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/5-cube_t1.svg/100px-5-cube_t1.svg.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/5-cube_t1.svg/150px-5-cube_t1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6b/5-cube_t1.svg/200px-5-cube_t1.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br />Rectified 5-cube<br /><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> </td> <td rowspan="2"><span typeof="mw:File"><a href="/wiki/File:5-cube_t2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/5-cube_t2.svg/150px-5-cube_t2.svg.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/5-cube_t2.svg/225px-5-cube_t2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/23/5-cube_t2.svg/300px-5-cube_t2.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Birectified_5-cube" class="mw-redirect" title="Birectified 5-cube">Birectified 5-cube</a><br />Birectified 5-orthoplex<br /><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> </td></tr> <tr align="center"> <td><span typeof="mw:File"><a href="/wiki/File:5-cube_t4.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/76/5-cube_t4.svg/100px-5-cube_t4.svg.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/76/5-cube_t4.svg/150px-5-cube_t4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/76/5-cube_t4.svg/200px-5-cube_t4.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/5-orthoplex" title="5-orthoplex">5-orthoplex</a><br /><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:5-cube_t3.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/5-cube_t3.svg/100px-5-cube_t3.svg.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/5-cube_t3.svg/150px-5-cube_t3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/38/5-cube_t3.svg/200px-5-cube_t3.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Rectified_5-orthoplex" class="mw-redirect" title="Rectified 5-orthoplex">Rectified 5-orthoplex</a><br /><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> </td></tr> <tr> <th colspan="5"><a href="/wiki/Orthogonal_projection" class="mw-redirect" title="Orthogonal projection">Orthogonal projections</a> in A<sub>5</sub> <a href="/wiki/Coxeter_plane" class="mw-redirect" title="Coxeter plane">Coxeter plane</a> </th></tr></tbody></table> <p>In five-dimensional <a href="/wiki/Geometry" title="Geometry">geometry</a>, a <b>rectified 5-cube</b> is a convex <a href="/wiki/Uniform_5-polytope" title="Uniform 5-polytope">uniform 5-polytope</a>, being a <a href="/wiki/Rectification_(geometry)" title="Rectification (geometry)">rectification</a> of the regular <a href="/wiki/5-cube" title="5-cube">5-cube</a>. </p><p>There are 5 degrees of rectifications of a 5-polytope, the zeroth here being the <a href="/wiki/5-cube" title="5-cube">5-cube</a>, and the 4th and last being the <a href="/wiki/5-orthoplex" title="5-orthoplex">5-orthoplex</a>. Vertices of the rectified 5-cube are located at the edge-centers of the 5-cube. Vertices of the birectified 5-cube are located in the square face centers of the 5-cube. </p> <div style="clear:both;" class=""></div> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Rectified_5-cube">Rectified 5-cube</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rectified_5-cubes&action=edit&section=1" title="Edit section: Rectified 5-cube"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style="float:right; margin-left:10px" width="280"> <tbody><tr> <th style="background-color:#e7dcc3" colspan="3">Rectified 5-cube<br />rectified penteract (rin) </th></tr> <tr> <td style="background-color:#e7dcc3">Type </td> <td colspan="2"><a href="/wiki/Uniform_5-polytope" title="Uniform 5-polytope">uniform 5-polytope</a> </td></tr> <tr> <td style="background-color:#e7dcc3"><a href="/wiki/Schl%C3%A4fli_symbol" title="Schläfli symbol">Schläfli symbol</a> </td> <td colspan="2">r{4,3,3,3} </td></tr> <tr> <td style="background-color:#e7dcc3"><a href="/wiki/Coxeter_diagram" class="mw-redirect" title="Coxeter diagram">Coxeter diagram</a> </td> <td colspan="2"><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> = <span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/4/4b/CDel_split1-43.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5b/CDel_3b.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/0/04/CDel_nodeb.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5b/CDel_3b.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/0/04/CDel_nodeb.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span></span><br /><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/56/CDel_nodes_11.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/3/32/CDel_split2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> </td></tr> <tr> <td style="background-color:#e7dcc3">4-faces</td> <td>42</td> <td>10 <span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> <span typeof="mw:File"><a href="/wiki/Rectified_tesseract" title="Rectified tesseract"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/4-cube_t1.svg/25px-4-cube_t1.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/4-cube_t1.svg/38px-4-cube_t1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/21/4-cube_t1.svg/50px-4-cube_t1.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br />32 <span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> <span typeof="mw:File"><a href="/wiki/5-cell" title="5-cell"><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></span> </td></tr> <tr> <td style="background-color:#e7dcc3">Cells</td> <td>200</td> <td>40 <span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> <span typeof="mw:File"><a href="/wiki/Cuboctahedron" title="Cuboctahedron"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/3-cube_t1.svg/25px-3-cube_t1.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/3-cube_t1.svg/38px-3-cube_t1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c5/3-cube_t1.svg/50px-3-cube_t1.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br />160 <span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> <span typeof="mw:File"><a href="/wiki/Tetrahedron" title="Tetrahedron"><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></span> </td></tr> <tr> <td style="background-color:#e7dcc3">Faces</td> <td>400</td> <td>80 <span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> <span typeof="mw:File"><a href="/wiki/Square" title="Square"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/2-cube.svg/25px-2-cube.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/2-cube.svg/38px-2-cube.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/2-cube.svg/50px-2-cube.svg.png 2x" data-file-width="800" data-file-height="800" /></a></span><br />320 <span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> <span typeof="mw:File"><a href="/wiki/Triangle" title="Triangle"><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></span> </td></tr> <tr> <td style="background-color:#e7dcc3">Edges </td> <td colspan="2">320 </td></tr> <tr> <td style="background-color:#e7dcc3">Vertices </td> <td colspan="2">80 </td></tr> <tr> <td style="background-color:#e7dcc3"><a href="/wiki/Vertex_figure" title="Vertex figure">Vertex figure</a> </td> <td colspan="2"><span typeof="mw:File"><a href="/wiki/File:Rectified_5-cube_verf.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Rectified_5-cube_verf.png/80px-Rectified_5-cube_verf.png" decoding="async" width="80" height="91" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Rectified_5-cube_verf.png/120px-Rectified_5-cube_verf.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Rectified_5-cube_verf.png/160px-Rectified_5-cube_verf.png 2x" data-file-width="605" data-file-height="690" /></a></span><br /><a href="/wiki/Tetrahedral_prism" title="Tetrahedral prism">Tetrahedral prism</a> </td></tr> <tr> <td style="background-color:#e7dcc3"><a href="/wiki/Coxeter_group" title="Coxeter group">Coxeter group</a> </td> <td colspan="2">B<sub>5</sub>, [4,3<sup>3</sup>], order 3840 </td></tr> <tr> <td style="background-color:#e7dcc3">Dual </td> <td colspan="2"> </td></tr> <tr> <td style="background-color:#e7dcc3">Base point </td> <td colspan="2">(0,1,1,1,1,1)√2 </td></tr> <tr> <td style="background-color:#e7dcc3"><a href="/wiki/Uniform_polytope#Circumradius" title="Uniform polytope">Circumradius</a> </td> <td colspan="2">sqrt(2) = 1.414214 </td></tr> <tr> <td style="background-color:#e7dcc3">Properties </td> <td colspan="2"><a href="/wiki/Convex_polytope" title="Convex polytope">convex</a>, <a href="/wiki/Isogonal_figure" title="Isogonal figure">isogonal</a> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Alternate_names">Alternate names</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rectified_5-cubes&action=edit&section=2" title="Edit section: Alternate names"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Rectified penteract (acronym: rin) (Jonathan Bowers)</li></ul> <div class="mw-heading mw-heading3"><h3 id="Construction">Construction</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rectified_5-cubes&action=edit&section=3" title="Edit section: Construction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The rectified 5-cube may be constructed from the <a href="/wiki/5-cube" title="5-cube">5-cube</a> by <a href="/wiki/Rectification_(geometry)" title="Rectification (geometry)">truncating</a> its vertices at the midpoints of its edges. </p> <div class="mw-heading mw-heading3"><h3 id="Coordinates">Coordinates</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rectified_5-cubes&action=edit&section=4" title="Edit section: Coordinates"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Cartesian_coordinates" class="mw-redirect" title="Cartesian coordinates">Cartesian coordinates</a> of the vertices of the rectified 5-cube with edge length <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4afc1e27d418021bf10898eb44a7f5f315735ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:3.009ex;" alt="{\displaystyle {\sqrt {2}}}"></span> is given by all permutations of: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (0,\ \pm 1,\ \pm 1,\ \pm 1,\ \pm 1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mtext> </mtext> <mo>±</mo> <mn>1</mn> <mo>,</mo> <mtext> </mtext> <mo>±</mo> <mn>1</mn> <mo>,</mo> <mtext> </mtext> <mo>±</mo> <mn>1</mn> <mo>,</mo> <mtext> </mtext> <mo>±</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (0,\ \pm 1,\ \pm 1,\ \pm 1,\ \pm 1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37ba049f65d9f0b90868d8f9d159d7b136006c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.442ex; height:2.843ex;" alt="{\displaystyle (0,\ \pm 1,\ \pm 1,\ \pm 1,\ \pm 1)}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Images">Images</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rectified_5-cubes&action=edit&section=5" title="Edit section: Images"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <caption><a href="/wiki/Orthographic_projection" title="Orthographic projection">orthographic projections</a> </caption> <tbody><tr style="text-align:center;"> <th><a href="/wiki/Coxeter_plane" class="mw-redirect" title="Coxeter plane">Coxeter plane</a> </th> <th>B<sub>5</sub> </th> <th>B<sub>4</sub> / D<sub>5</sub> </th> <th>B<sub>3</sub> / D<sub>4</sub> / A<sub>2</sub> </th></tr> <tr style="text-align:center;"> <th>Graph </th> <td><span typeof="mw:File"><a href="/wiki/File:5-cube_t1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/5-cube_t1.svg/150px-5-cube_t1.svg.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/5-cube_t1.svg/225px-5-cube_t1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6b/5-cube_t1.svg/300px-5-cube_t1.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:5-cube_t1_B4.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/5-cube_t1_B4.svg/150px-5-cube_t1_B4.svg.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/5-cube_t1_B4.svg/225px-5-cube_t1_B4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/5-cube_t1_B4.svg/300px-5-cube_t1_B4.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:5-cube_t1_B3.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/5-cube_t1_B3.svg/150px-5-cube_t1_B3.svg.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/5-cube_t1_B3.svg/225px-5-cube_t1_B3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d9/5-cube_t1_B3.svg/300px-5-cube_t1_B3.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span> </td></tr> <tr style="text-align:center;"> <th><a href="/wiki/Dihedral_symmetry" class="mw-redirect" title="Dihedral symmetry">Dihedral symmetry</a> </th> <td>[10] </td> <td>[8] </td> <td>[6] </td></tr> <tr style="text-align:center;"> <th>Coxeter plane </th> <th>B<sub>2</sub> </th> <th>A<sub>3</sub> </th></tr> <tr style="text-align:center;"> <th>Graph </th> <td><span typeof="mw:File"><a href="/wiki/File:5-cube_t1_B2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/5-cube_t1_B2.svg/150px-5-cube_t1_B2.svg.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/5-cube_t1_B2.svg/225px-5-cube_t1_B2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e7/5-cube_t1_B2.svg/300px-5-cube_t1_B2.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:5-cube_t1_A3.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b7/5-cube_t1_A3.svg/150px-5-cube_t1_A3.svg.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b7/5-cube_t1_A3.svg/225px-5-cube_t1_A3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b7/5-cube_t1_A3.svg/300px-5-cube_t1_A3.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span> </td></tr> <tr style="text-align:center;"> <th>Dihedral symmetry </th> <td>[4] </td> <td>[4] </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Birectified_5-cube">Birectified 5-cube</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rectified_5-cubes&action=edit&section=6" title="Edit section: Birectified 5-cube"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style="float:right; margin-left:10px" width="280"> <tbody><tr> <th style="background-color:#e7dcc3" colspan="3">Birectified 5-cube<br />birectified penteract (nit) </th></tr> <tr> <td style="background-color:#e7dcc3">Type </td> <td colspan="2"><a href="/wiki/Uniform_5-polytope" title="Uniform 5-polytope">uniform 5-polytope</a> </td></tr> <tr> <td style="background-color:#e7dcc3"><a href="/wiki/Schl%C3%A4fli_symbol" title="Schläfli symbol">Schläfli symbol</a> </td> <td colspan="2">2r{4,3,3,3} </td></tr> <tr> <td style="background-color:#e7dcc3"><a href="/wiki/Coxeter_diagram" class="mw-redirect" title="Coxeter diagram">Coxeter diagram</a> </td> <td colspan="2"><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> = <span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/a/a1/CDel_split1.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/f/f6/CDel_4a3b.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span></span><br /><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/3/32/CDel_split2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> </td></tr> <tr> <td style="background-color:#e7dcc3">4-faces</td> <td>42</td> <td>10 <span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> <span typeof="mw:File"><a href="/wiki/24-cell" title="24-cell"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/24-cell_t0_B4.svg/25px-24-cell_t0_B4.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/24-cell_t0_B4.svg/38px-24-cell_t0_B4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b5/24-cell_t0_B4.svg/50px-24-cell_t0_B4.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br />32 <span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> <span typeof="mw:File"><a href="/wiki/Rectified_5-cell" title="Rectified 5-cell"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/4-simplex_t1.svg/25px-4-simplex_t1.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/4-simplex_t1.svg/38px-4-simplex_t1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1f/4-simplex_t1.svg/50px-4-simplex_t1.svg.png 2x" data-file-width="3200" data-file-height="3200" /></a></span> </td></tr> <tr> <td style="background-color:#e7dcc3">Cells</td> <td>280</td> <td>40 <span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> <span typeof="mw:File"><a href="/wiki/Octahedron" title="Octahedron"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/3-cube_t2.svg/25px-3-cube_t2.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/3-cube_t2.svg/38px-3-cube_t2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/79/3-cube_t2.svg/50px-3-cube_t2.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br />160 <span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> <span typeof="mw:File"><a href="/wiki/Octahedron" title="Octahedron"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/3-simplex_t1.svg/25px-3-simplex_t1.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/3-simplex_t1.svg/38px-3-simplex_t1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0f/3-simplex_t1.svg/50px-3-simplex_t1.svg.png 2x" data-file-width="3200" data-file-height="3200" /></a></span><br />80 <span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> <span typeof="mw:File"><a href="/wiki/Tetrahedron" title="Tetrahedron"><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></span> </td></tr> <tr> <td style="background-color:#e7dcc3">Faces</td> <td>640</td> <td>320 <span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> <span typeof="mw:File"><a href="/wiki/Triangle" title="Triangle"><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></span><br />320 <span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span></span> <span typeof="mw:File"><a href="/wiki/Triangle" title="Triangle"><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></span> </td></tr> <tr> <td style="background-color:#e7dcc3">Edges </td> <td colspan="2">480 </td></tr> <tr> <td style="background-color:#e7dcc3">Vertices </td> <td colspan="2">80 </td></tr> <tr> <td style="background-color:#e7dcc3"><a href="/wiki/Vertex_figure" title="Vertex figure">Vertex figure</a> </td> <td colspan="2"><span typeof="mw:File"><a href="/wiki/File:Birectified_penteract_verf.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Birectified_penteract_verf.png/80px-Birectified_penteract_verf.png" decoding="async" width="80" height="76" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Birectified_penteract_verf.png/120px-Birectified_penteract_verf.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Birectified_penteract_verf.png/160px-Birectified_penteract_verf.png 2x" data-file-width="503" data-file-height="476" /></a></span><br /><a href="/wiki/3-4_duoprism" title="3-4 duoprism">{3}×{4}</a> </td></tr> <tr> <td style="background-color:#e7dcc3"><a href="/wiki/Coxeter_group" title="Coxeter group">Coxeter group</a> </td> <td colspan="2">B<sub>5</sub>, [4,3<sup>3</sup>], order 3840<br />D<sub>5</sub>, [3<sup>2,1,1</sup>], order 1920 </td></tr> <tr> <td style="background-color:#e7dcc3">Dual </td> <td colspan="2"> </td></tr> <tr> <td style="background-color:#e7dcc3">Base point </td> <td colspan="2">(0,0,1,1,1,1)√2 </td></tr> <tr> <td style="background-color:#e7dcc3"><a href="/wiki/Uniform_polytope#Circumradius" title="Uniform polytope">Circumradius</a> </td> <td colspan="2">sqrt(3/2) = 1.224745 </td></tr> <tr> <td style="background-color:#e7dcc3">Properties </td> <td colspan="2"><a href="/wiki/Convex_polytope" title="Convex polytope">convex</a>, <a href="/wiki/Isogonal_figure" title="Isogonal figure">isogonal</a> </td></tr></tbody></table> <p><a href="/wiki/Emanuel_Lodewijk_Elte" title="Emanuel Lodewijk Elte">E. L. Elte</a> identified it in 1912 as a semiregular polytope, identifying it as Cr<sub>5</sub><sup>2</sup> as a second rectification of a 5-dimensional <a href="/wiki/Cross_polytope" class="mw-redirect" title="Cross polytope">cross polytope</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Alternate_names_2">Alternate names</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rectified_5-cubes&action=edit&section=7" title="Edit section: Alternate names"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Birectified 5-cube/penteract</li> <li>Birectified pentacross/5-orthoplex/triacontiditeron</li> <li>Penteractitriacontiditeron (acronym: nit) (Jonathan Bowers)</li> <li>Rectified 5-demicube/demipenteract</li></ul> <div class="mw-heading mw-heading3"><h3 id="Construction_and_coordinates">Construction and coordinates</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rectified_5-cubes&action=edit&section=8" title="Edit section: Construction and coordinates"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <i>birectified 5-cube</i> may be constructed by <a href="/wiki/Rectification_(geometry)" title="Rectification (geometry)">birectifying</a> the vertices of the <a href="/wiki/5-cube" title="5-cube">5-cube</a> at <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4afc1e27d418021bf10898eb44a7f5f315735ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:3.009ex;" alt="{\displaystyle {\sqrt {2}}}"></span> of the edge length. </p><p>The <a href="/wiki/Cartesian_coordinate" class="mw-redirect" title="Cartesian coordinate">Cartesian coordinates</a> of the vertices of a <i>birectified 5-cube</i> having edge length 2 are all permutations of: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(0,\ 0,\ \pm 1,\ \pm 1,\ \pm 1\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mo>,</mo> <mtext> </mtext> <mn>0</mn> <mo>,</mo> <mtext> </mtext> <mo>±</mo> <mn>1</mn> <mo>,</mo> <mtext> </mtext> <mo>±</mo> <mn>1</mn> <mo>,</mo> <mtext> </mtext> <mo>±</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(0,\ 0,\ \pm 1,\ \pm 1,\ \pm 1\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d51f11c078da773746259d4aa173957fa2b4849" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.601ex; height:2.843ex;" alt="{\displaystyle \left(0,\ 0,\ \pm 1,\ \pm 1,\ \pm 1\right)}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Images_2">Images</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rectified_5-cubes&action=edit&section=9" title="Edit section: Images"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <caption><a href="/wiki/Orthographic_projection" title="Orthographic projection">orthographic projections</a> </caption> <tbody><tr style="text-align:center;"> <th><a href="/wiki/Coxeter_plane" class="mw-redirect" title="Coxeter plane">Coxeter plane</a> </th> <th>B<sub>5</sub> </th> <th>B<sub>4</sub> / D<sub>5</sub> </th> <th>B<sub>3</sub> / D<sub>4</sub> / A<sub>2</sub> </th></tr> <tr style="text-align:center;"> <th>Graph </th> <td><span typeof="mw:File"><a href="/wiki/File:5-cube_t2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/5-cube_t2.svg/150px-5-cube_t2.svg.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/5-cube_t2.svg/225px-5-cube_t2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/23/5-cube_t2.svg/300px-5-cube_t2.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:5-cube_t2_B4.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/5-cube_t2_B4.svg/150px-5-cube_t2_B4.svg.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/5-cube_t2_B4.svg/225px-5-cube_t2_B4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ec/5-cube_t2_B4.svg/300px-5-cube_t2_B4.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:5-cube_t2_B3.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/5-cube_t2_B3.svg/150px-5-cube_t2_B3.svg.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/5-cube_t2_B3.svg/225px-5-cube_t2_B3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/46/5-cube_t2_B3.svg/300px-5-cube_t2_B3.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span> </td></tr> <tr style="text-align:center;"> <th><a href="/wiki/Dihedral_symmetry" class="mw-redirect" title="Dihedral symmetry">Dihedral symmetry</a> </th> <td>[10] </td> <td>[8] </td> <td>[6] </td></tr> <tr style="text-align:center;"> <th>Coxeter plane </th> <th>B<sub>2</sub> </th> <th>A<sub>3</sub> </th></tr> <tr style="text-align:center;"> <th>Graph </th> <td><span typeof="mw:File"><a href="/wiki/File:5-cube_t2_B2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/5-cube_t2_B2.svg/150px-5-cube_t2_B2.svg.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/5-cube_t2_B2.svg/225px-5-cube_t2_B2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5a/5-cube_t2_B2.svg/300px-5-cube_t2_B2.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:5-cube_t2_A3.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/5-cube_t2_A3.svg/150px-5-cube_t2_A3.svg.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/5-cube_t2_A3.svg/225px-5-cube_t2_A3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/5-cube_t2_A3.svg/300px-5-cube_t2_A3.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span> </td></tr> <tr style="text-align:center;"> <th>Dihedral symmetry </th> <td>[4] </td> <td>[4] </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Related_polytopes">Related polytopes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rectified_5-cubes&action=edit&section=10" title="Edit section: Related polytopes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <caption>2-isotopic hypercubes </caption> <tbody><tr style="text-align:center;"> <th>Dim. </th> <th>2 </th> <th>3 </th> <th>4 </th> <th>5 </th> <th>6 </th> <th>7 </th> <th>8 </th> <th><i>n</i> </th></tr> <tr style="text-align:center;"> <th>Name </th> <td><a href="/wiki/Octagon" title="Octagon">t{4}</a> </td> <td><a href="/wiki/Cuboctahedron" title="Cuboctahedron">r{4,3}</a> </td> <td><a href="/wiki/Bitruncated_tesseract" class="mw-redirect" title="Bitruncated tesseract">2t{4,3,3}</a> </td> <td><a href="/wiki/Birectified_5-cube" class="mw-redirect" title="Birectified 5-cube">2r{4,3,3,3}</a> </td> <td><a href="/wiki/Tritruncated_6-cube" class="mw-redirect" title="Tritruncated 6-cube">3t{4,3,3,3,3}</a> </td> <td><a href="/wiki/Trirectified_7-cube" class="mw-redirect" title="Trirectified 7-cube">3r{4,3,3,3,3,3}</a> </td> <td><a href="/wiki/Quadritruncated_8-cube" class="mw-redirect" title="Quadritruncated 8-cube">4t{4,3,3,3,3,3,3}</a> </td> <td rowspan="5">... </td></tr> <tr style="text-align:center;"> <th><a href="/wiki/Coxeter_diagram" class="mw-redirect" title="Coxeter diagram">Coxeter<br />diagram</a> </th> <td><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/9/90/CDel_label4.png" decoding="async" width="7" height="23" class="mw-file-element" data-file-width="7" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/f/fc/CDel_branch_11.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span></span> </td> <td><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/4/4b/CDel_split1-43.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span></span> </td> <td><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/f/fc/CDel_branch_11.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/f/f6/CDel_4a3b.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span></span> </td> <td><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/a/a1/CDel_split1.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/f/f6/CDel_4a3b.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span></span> </td> <td><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/f/fc/CDel_branch_11.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/d/d5/CDel_3ab.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/f/f6/CDel_4a3b.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span></span> </td> <td><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><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" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/a/a1/CDel_split1.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/d/d5/CDel_3ab.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/f/f6/CDel_4a3b.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span></span> </td> <td><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/f/fc/CDel_branch_11.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/d/d5/CDel_3ab.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/d/d5/CDel_3ab.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/f/f6/CDel_4a3b.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span></span> </td></tr> <tr style="text-align:center;"> <th>Images </th> <td><span typeof="mw:File"><a href="/wiki/File:Truncated_square.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Truncated_square.png/60px-Truncated_square.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Truncated_square.png/90px-Truncated_square.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Truncated_square.png/120px-Truncated_square.png 2x" data-file-width="388" data-file-height="386" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:3-cube_t1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/3-cube_t1.svg/60px-3-cube_t1.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/3-cube_t1.svg/90px-3-cube_t1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c5/3-cube_t1.svg/120px-3-cube_t1.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><span typeof="mw:File"><a href="/wiki/File:Cuboctahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Cuboctahedron.png/60px-Cuboctahedron.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Cuboctahedron.png/90px-Cuboctahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Cuboctahedron.png/120px-Cuboctahedron.png 2x" data-file-width="1000" data-file-height="1000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:4-cube_t12.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/4-cube_t12.svg/60px-4-cube_t12.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/4-cube_t12.svg/90px-4-cube_t12.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/90/4-cube_t12.svg/120px-4-cube_t12.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><span typeof="mw:File"><a href="/wiki/File:Schlegel_half-solid_bitruncated_8-cell.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Schlegel_half-solid_bitruncated_8-cell.png/60px-Schlegel_half-solid_bitruncated_8-cell.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Schlegel_half-solid_bitruncated_8-cell.png/90px-Schlegel_half-solid_bitruncated_8-cell.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Schlegel_half-solid_bitruncated_8-cell.png/120px-Schlegel_half-solid_bitruncated_8-cell.png 2x" data-file-width="1000" data-file-height="1000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:5-cube_t2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/5-cube_t2.svg/60px-5-cube_t2.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/5-cube_t2.svg/90px-5-cube_t2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/23/5-cube_t2.svg/120px-5-cube_t2.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><span typeof="mw:File"><a href="/wiki/File:5-cube_t2_A3.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/5-cube_t2_A3.svg/60px-5-cube_t2_A3.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/5-cube_t2_A3.svg/90px-5-cube_t2_A3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/5-cube_t2_A3.svg/120px-5-cube_t2_A3.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:6-cube_t23.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/6-cube_t23.svg/60px-6-cube_t23.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/6-cube_t23.svg/90px-6-cube_t23.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/17/6-cube_t23.svg/120px-6-cube_t23.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><span typeof="mw:File"><a href="/wiki/File:6-cube_t23_A5.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/6-cube_t23_A5.svg/60px-6-cube_t23_A5.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/6-cube_t23_A5.svg/90px-6-cube_t23_A5.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e8/6-cube_t23_A5.svg/120px-6-cube_t23_A5.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:7-cube_t3.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/7-cube_t3.svg/60px-7-cube_t3.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/7-cube_t3.svg/90px-7-cube_t3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b5/7-cube_t3.svg/120px-7-cube_t3.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><span typeof="mw:File"><a href="/wiki/File:7-cube_t3_A5.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/7-cube_t3_A5.svg/60px-7-cube_t3_A5.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/7-cube_t3_A5.svg/90px-7-cube_t3_A5.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/7-cube_t3_A5.svg/120px-7-cube_t3_A5.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:8-cube_t34.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/8-cube_t34.svg/60px-8-cube_t34.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/8-cube_t34.svg/90px-8-cube_t34.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/8-cube_t34.svg/120px-8-cube_t34.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><span typeof="mw:File"><a href="/wiki/File:8-cube_t34_A7.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/8-cube_t34_A7.svg/60px-8-cube_t34_A7.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/8-cube_t34_A7.svg/90px-8-cube_t34_A7.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9d/8-cube_t34_A7.svg/120px-8-cube_t34_A7.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span> </td></tr> <tr style="text-align:center;"> <th>Facets </th> <td> </td> <td><a href="/wiki/Triangle" title="Triangle">{3}</a> <span typeof="mw:File"><a href="/wiki/File:Regular_polygon_3_annotated.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Regular_polygon_3_annotated.svg/30px-Regular_polygon_3_annotated.svg.png" decoding="async" width="30" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Regular_polygon_3_annotated.svg/45px-Regular_polygon_3_annotated.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Regular_polygon_3_annotated.svg/60px-Regular_polygon_3_annotated.svg.png 2x" data-file-width="503" data-file-height="509" /></a></span><br /><a href="/wiki/Square" title="Square">{4}</a> <span typeof="mw:File"><a href="/wiki/File:Regular_polygon_4_annotated.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Regular_polygon_4_annotated.svg/30px-Regular_polygon_4_annotated.svg.png" decoding="async" width="30" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Regular_polygon_4_annotated.svg/45px-Regular_polygon_4_annotated.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Regular_polygon_4_annotated.svg/60px-Regular_polygon_4_annotated.svg.png 2x" data-file-width="515" data-file-height="515" /></a></span> </td> <td><a href="/wiki/Truncated_tetrahedron" title="Truncated tetrahedron">t{3,3}</a> <span typeof="mw:File"><a href="/wiki/File:Uniform_polyhedron-33-t01.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Uniform_polyhedron-33-t01.png/30px-Uniform_polyhedron-33-t01.png" decoding="async" width="30" height="32" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Uniform_polyhedron-33-t01.png/45px-Uniform_polyhedron-33-t01.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Uniform_polyhedron-33-t01.png/60px-Uniform_polyhedron-33-t01.png 2x" data-file-width="688" data-file-height="728" /></a></span><br /><a href="/wiki/Truncated_octahedron" title="Truncated octahedron">t{3,4}</a> <span typeof="mw:File"><a href="/wiki/File:Uniform_polyhedron-43-t12.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Uniform_polyhedron-43-t12.png/30px-Uniform_polyhedron-43-t12.png" decoding="async" width="30" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Uniform_polyhedron-43-t12.png/45px-Uniform_polyhedron-43-t12.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/59/Uniform_polyhedron-43-t12.png/60px-Uniform_polyhedron-43-t12.png 2x" data-file-width="800" data-file-height="800" /></a></span> </td> <td><a href="/wiki/Rectified_5-cell" title="Rectified 5-cell">r{3,3,3}</a> <span typeof="mw:File"><a href="/wiki/File:Schlegel_half-solid_rectified_5-cell.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Schlegel_half-solid_rectified_5-cell.png/30px-Schlegel_half-solid_rectified_5-cell.png" decoding="async" width="30" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Schlegel_half-solid_rectified_5-cell.png/45px-Schlegel_half-solid_rectified_5-cell.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/01/Schlegel_half-solid_rectified_5-cell.png/60px-Schlegel_half-solid_rectified_5-cell.png 2x" data-file-width="1001" data-file-height="999" /></a></span><br /><a href="/wiki/Rectified_16-cell" class="mw-redirect" title="Rectified 16-cell">r{3,3,4}</a> <span typeof="mw:File"><a href="/wiki/File:Schlegel_wireframe_24-cell.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Schlegel_wireframe_24-cell.png/30px-Schlegel_wireframe_24-cell.png" decoding="async" width="30" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Schlegel_wireframe_24-cell.png/45px-Schlegel_wireframe_24-cell.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/77/Schlegel_wireframe_24-cell.png/60px-Schlegel_wireframe_24-cell.png 2x" data-file-width="862" data-file-height="816" /></a></span> </td> <td><a href="/wiki/Bitruncated_5-simplex" class="mw-redirect" title="Bitruncated 5-simplex">2t{3,3,3,3}</a> <span typeof="mw:File"><a href="/wiki/File:5-simplex_t12.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/5-simplex_t12.svg/30px-5-simplex_t12.svg.png" decoding="async" width="30" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/5-simplex_t12.svg/45px-5-simplex_t12.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/5-simplex_t12.svg/60px-5-simplex_t12.svg.png 2x" data-file-width="3200" data-file-height="3200" /></a></span><br /><a href="/wiki/Bitruncated_5-orthoplex" class="mw-redirect" title="Bitruncated 5-orthoplex">2t{3,3,3,4}</a> <span typeof="mw:File"><a href="/wiki/File:5-cube_t23.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/5-cube_t23.svg/30px-5-cube_t23.svg.png" decoding="async" width="30" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/5-cube_t23.svg/45px-5-cube_t23.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/98/5-cube_t23.svg/60px-5-cube_t23.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span> </td> <td><a href="/wiki/Birectified_6-simplex" class="mw-redirect" title="Birectified 6-simplex">2r{3,3,3,3,3}</a> <span typeof="mw:File"><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/30px-6-simplex_t2.svg.png" decoding="async" width="30" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b3/6-simplex_t2.svg/45px-6-simplex_t2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b3/6-simplex_t2.svg/60px-6-simplex_t2.svg.png 2x" data-file-width="3200" data-file-height="3200" /></a></span><br /><a href="/wiki/Birectified_6-orthoplex" class="mw-redirect" title="Birectified 6-orthoplex">2r{3,3,3,3,4}</a> <span typeof="mw:File"><a href="/wiki/File:6-cube_t4.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/6-cube_t4.svg/30px-6-cube_t4.svg.png" decoding="async" width="30" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/6-cube_t4.svg/45px-6-cube_t4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a6/6-cube_t4.svg/60px-6-cube_t4.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span> </td> <td><a href="/wiki/Tritruncated_7-simplex" class="mw-redirect" title="Tritruncated 7-simplex">3t{3,3,3,3,3,3}</a> <span typeof="mw:File"><a href="/wiki/File:7-simplex_t23.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/7-simplex_t23.svg/30px-7-simplex_t23.svg.png" decoding="async" width="30" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/7-simplex_t23.svg/45px-7-simplex_t23.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/44/7-simplex_t23.svg/60px-7-simplex_t23.svg.png 2x" data-file-width="3200" data-file-height="3200" /></a></span><br /><a href="/wiki/Tritruncated_7-orthoplex" class="mw-redirect" title="Tritruncated 7-orthoplex">3t{3,3,3,3,3,4}</a> <span typeof="mw:File"><a href="/wiki/File:7-cube_t45.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/7-cube_t45.svg/30px-7-cube_t45.svg.png" decoding="async" width="30" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/7-cube_t45.svg/45px-7-cube_t45.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/79/7-cube_t45.svg/60px-7-cube_t45.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span> </td></tr> <tr style="text-align:center;vertical-align:bottom;"> <th><a href="/wiki/Vertex_figure" title="Vertex figure">Vertex<br />figure</a> </th> <td>( )v( ) </td> <td><span typeof="mw:File"><a href="/wiki/File:Cuboctahedron_vertfig.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/Cuboctahedron_vertfig.png/60px-Cuboctahedron_vertfig.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/Cuboctahedron_vertfig.png/90px-Cuboctahedron_vertfig.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/61/Cuboctahedron_vertfig.png/120px-Cuboctahedron_vertfig.png 2x" data-file-width="600" data-file-height="600" /></a></span><br /><a href="/wiki/Rectangle" title="Rectangle">{ }×{ }</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Bitruncated_8-cell_verf.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Bitruncated_8-cell_verf.png/60px-Bitruncated_8-cell_verf.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Bitruncated_8-cell_verf.png/90px-Bitruncated_8-cell_verf.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/69/Bitruncated_8-cell_verf.png/120px-Bitruncated_8-cell_verf.png 2x" data-file-width="180" data-file-height="180" /></a></span><br /><a href="/wiki/Disphenoid" title="Disphenoid">{ }v{ }</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Birectified_penteract_verf.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Birectified_penteract_verf.png/60px-Birectified_penteract_verf.png" decoding="async" width="60" height="57" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Birectified_penteract_verf.png/90px-Birectified_penteract_verf.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Birectified_penteract_verf.png/120px-Birectified_penteract_verf.png 2x" data-file-width="503" data-file-height="476" /></a></span><br /><a href="/wiki/3-4_duoprism" title="3-4 duoprism">{3}×{4}</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Tritruncated_6-cube_verf.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Tritruncated_6-cube_verf.png/60px-Tritruncated_6-cube_verf.png" decoding="async" width="60" height="61" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Tritruncated_6-cube_verf.png/90px-Tritruncated_6-cube_verf.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/53/Tritruncated_6-cube_verf.png/120px-Tritruncated_6-cube_verf.png 2x" data-file-width="849" data-file-height="866" /></a></span><br />{3}v{4} </td> <td>{3,3}×{3,4} </td> <td>{3,3}v{3,4} </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Related_polytopes_2">Related polytopes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rectified_5-cubes&action=edit&section=11" title="Edit section: Related polytopes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>These polytopes are a part of 31 <a href="/wiki/Uniform_polyteron#Uniform_polyteron" class="mw-redirect" title="Uniform polyteron">uniform polytera</a> generated from the regular <a href="/wiki/5-cube" title="5-cube">5-cube</a> or <a href="/wiki/5-orthoplex" title="5-orthoplex">5-orthoplex</a>. </p> <table class="wikitable mw-collapsible mw-collapsed"> <tbody><tr> <th colspan="12">B5 polytopes </th></tr> <tr style="text-align:center;"> <td bgcolor="#fff0f0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t4.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/76/5-cube_t4.svg/80px-5-cube_t4.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/76/5-cube_t4.svg/120px-5-cube_t4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/76/5-cube_t4.svg/160px-5-cube_t4.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/5-orthoplex" title="5-orthoplex">β<sub>5</sub></a> </td> <td bgcolor="#fff0f0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t3.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/5-cube_t3.svg/80px-5-cube_t3.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/5-cube_t3.svg/120px-5-cube_t3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/38/5-cube_t3.svg/160px-5-cube_t3.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Rectified_5-orthoplex" class="mw-redirect" title="Rectified 5-orthoplex">t<sub>1</sub>β<sub>5</sub></a> </td> <td bgcolor="#f0fff0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/5-cube_t2.svg/80px-5-cube_t2.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/5-cube_t2.svg/120px-5-cube_t2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/23/5-cube_t2.svg/160px-5-cube_t2.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Birectified_5-cube" class="mw-redirect" title="Birectified 5-cube">t<sub>2</sub>γ<sub>5</sub></a> </td> <td bgcolor="#fff0f0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/5-cube_t1.svg/80px-5-cube_t1.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/5-cube_t1.svg/120px-5-cube_t1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6b/5-cube_t1.svg/160px-5-cube_t1.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Rectified_5-cube" class="mw-redirect" title="Rectified 5-cube">t<sub>1</sub>γ<sub>5</sub></a> </td> <td bgcolor="#fff0f0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t0.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/5-cube_t0.svg/80px-5-cube_t0.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/5-cube_t0.svg/120px-5-cube_t0.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b1/5-cube_t0.svg/160px-5-cube_t0.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/5-cube" title="5-cube">γ<sub>5</sub></a> </td> <td bgcolor="#f0f0ff"><span typeof="mw:File"><a href="/wiki/File:5-cube_t34.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/5-cube_t34.svg/80px-5-cube_t34.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/5-cube_t34.svg/120px-5-cube_t34.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/44/5-cube_t34.svg/160px-5-cube_t34.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Truncated_5-orthoplex" class="mw-redirect" title="Truncated 5-orthoplex">t<sub>0,1</sub>β<sub>5</sub></a> </td> <td bgcolor="#f0f0ff"><span typeof="mw:File"><a href="/wiki/File:5-cube_t24.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/5-cube_t24.svg/80px-5-cube_t24.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/5-cube_t24.svg/120px-5-cube_t24.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/5-cube_t24.svg/160px-5-cube_t24.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Cantellated_5-orthoplex" class="mw-redirect" title="Cantellated 5-orthoplex">t<sub>0,2</sub>β<sub>5</sub></a> </td> <td bgcolor="#f0f0ff"><span typeof="mw:File"><a href="/wiki/File:5-cube_t23.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/5-cube_t23.svg/80px-5-cube_t23.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/5-cube_t23.svg/120px-5-cube_t23.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/98/5-cube_t23.svg/160px-5-cube_t23.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Bitruncated_5-orthoplex" class="mw-redirect" title="Bitruncated 5-orthoplex">t<sub>1,2</sub>β<sub>5</sub></a> </td></tr> <tr style="text-align:center;"> <td bgcolor="#f0f0ff"><span typeof="mw:File"><a href="/wiki/File:5-cube_t14.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/09/5-cube_t14.svg/80px-5-cube_t14.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/09/5-cube_t14.svg/120px-5-cube_t14.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/09/5-cube_t14.svg/160px-5-cube_t14.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Runcinated_5-orthoplex" class="mw-redirect" title="Runcinated 5-orthoplex">t<sub>0,3</sub>β<sub>5</sub></a> </td> <td bgcolor="#f0fff0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t13.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/5-cube_t13.svg/80px-5-cube_t13.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/5-cube_t13.svg/120px-5-cube_t13.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/5-cube_t13.svg/160px-5-cube_t13.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Bicantellated_5-cube" class="mw-redirect" title="Bicantellated 5-cube">t<sub>1,3</sub>γ<sub>5</sub></a> </td> <td bgcolor="#fff0f0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t12.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/5-cube_t12.svg/80px-5-cube_t12.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/5-cube_t12.svg/120px-5-cube_t12.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8b/5-cube_t12.svg/160px-5-cube_t12.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Bitruncated_5-cube" class="mw-redirect" title="Bitruncated 5-cube">t<sub>1,2</sub>γ<sub>5</sub></a> </td> <td bgcolor="#f0fff0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t04.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/5-cube_t04.svg/80px-5-cube_t04.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/5-cube_t04.svg/120px-5-cube_t04.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/32/5-cube_t04.svg/160px-5-cube_t04.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Stericated_5-cube" class="mw-redirect" title="Stericated 5-cube">t<sub>0,4</sub>γ<sub>5</sub></a> </td> <td bgcolor="#fff0f0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t03.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b2/5-cube_t03.svg/80px-5-cube_t03.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b2/5-cube_t03.svg/120px-5-cube_t03.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b2/5-cube_t03.svg/160px-5-cube_t03.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Runcinated_5-cube" class="mw-redirect" title="Runcinated 5-cube">t<sub>0,3</sub>γ<sub>5</sub></a> </td> <td bgcolor="#fff0f0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t02.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/5-cube_t02.svg/80px-5-cube_t02.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/5-cube_t02.svg/120px-5-cube_t02.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0f/5-cube_t02.svg/160px-5-cube_t02.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Cantellated_5-cube" class="mw-redirect" title="Cantellated 5-cube">t<sub>0,2</sub>γ<sub>5</sub></a> </td> <td bgcolor="#fff0f0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t01.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/5-cube_t01.svg/80px-5-cube_t01.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/5-cube_t01.svg/120px-5-cube_t01.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/5-cube_t01.svg/160px-5-cube_t01.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Truncated_5-cube" class="mw-redirect" title="Truncated 5-cube">t<sub>0,1</sub>γ<sub>5</sub></a> </td> <td bgcolor="#f0f0ff"><span typeof="mw:File"><a href="/wiki/File:5-cube_t234.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/5-cube_t234.svg/80px-5-cube_t234.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/5-cube_t234.svg/120px-5-cube_t234.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ea/5-cube_t234.svg/160px-5-cube_t234.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Cantitruncated_5-orthoplex" class="mw-redirect" title="Cantitruncated 5-orthoplex">t<sub>0,1,2</sub>β<sub>5</sub></a> </td></tr> <tr style="text-align:center;"> <td bgcolor="#f0f0ff"><span typeof="mw:File"><a href="/wiki/File:5-cube_t134.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/5-cube_t134.svg/80px-5-cube_t134.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/5-cube_t134.svg/120px-5-cube_t134.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d3/5-cube_t134.svg/160px-5-cube_t134.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Runcitruncated_5-orthoplex" class="mw-redirect" title="Runcitruncated 5-orthoplex">t<sub>0,1,3</sub>β<sub>5</sub></a> </td> <td bgcolor="#f0f0ff"><span typeof="mw:File"><a href="/wiki/File:5-cube_t124.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/5-cube_t124.svg/80px-5-cube_t124.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/5-cube_t124.svg/120px-5-cube_t124.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/26/5-cube_t124.svg/160px-5-cube_t124.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Runcicantellated_5-orthoplex" class="mw-redirect" title="Runcicantellated 5-orthoplex">t<sub>0,2,3</sub>β<sub>5</sub></a> </td> <td bgcolor="#f0fff0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t123.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/5-cube_t123.svg/80px-5-cube_t123.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/5-cube_t123.svg/120px-5-cube_t123.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/15/5-cube_t123.svg/160px-5-cube_t123.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Bicantitruncated_5-cube" class="mw-redirect" title="Bicantitruncated 5-cube">t<sub>1,2,3</sub>γ<sub>5</sub></a> </td> <td bgcolor="#f0f0ff"><span typeof="mw:File"><a href="/wiki/File:5-cube_t034.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/5-cube_t034.svg/80px-5-cube_t034.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/5-cube_t034.svg/120px-5-cube_t034.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b9/5-cube_t034.svg/160px-5-cube_t034.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Steritruncated_5-orthoplex" class="mw-redirect" title="Steritruncated 5-orthoplex">t<sub>0,1,4</sub>β<sub>5</sub></a> </td> <td bgcolor="#f0fff0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t024.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/5-cube_t024.svg/80px-5-cube_t024.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/5-cube_t024.svg/120px-5-cube_t024.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e8/5-cube_t024.svg/160px-5-cube_t024.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Stericantellated_5-cube" class="mw-redirect" title="Stericantellated 5-cube">t<sub>0,2,4</sub>γ<sub>5</sub></a> </td> <td bgcolor="#fff0f0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t023.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/5-cube_t023.svg/80px-5-cube_t023.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/5-cube_t023.svg/120px-5-cube_t023.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fe/5-cube_t023.svg/160px-5-cube_t023.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Runcicantellated_5-cube" class="mw-redirect" title="Runcicantellated 5-cube">t<sub>0,2,3</sub>γ<sub>5</sub></a> </td> <td bgcolor="#fff0f0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t014.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/5-cube_t014.svg/80px-5-cube_t014.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/5-cube_t014.svg/120px-5-cube_t014.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/57/5-cube_t014.svg/160px-5-cube_t014.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Steritruncated_5-cube" class="mw-redirect" title="Steritruncated 5-cube">t<sub>0,1,4</sub>γ<sub>5</sub></a> </td> <td bgcolor="#fff0f0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t013.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/5-cube_t013.svg/80px-5-cube_t013.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/5-cube_t013.svg/120px-5-cube_t013.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/5-cube_t013.svg/160px-5-cube_t013.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Runcitruncated_5-cube" class="mw-redirect" title="Runcitruncated 5-cube">t<sub>0,1,3</sub>γ<sub>5</sub></a> </td></tr> <tr style="text-align:center;"> <td bgcolor="#fff0f0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t012.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/43/5-cube_t012.svg/80px-5-cube_t012.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/43/5-cube_t012.svg/120px-5-cube_t012.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/43/5-cube_t012.svg/160px-5-cube_t012.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Cantitruncated_5-cube" class="mw-redirect" title="Cantitruncated 5-cube">t<sub>0,1,2</sub>γ<sub>5</sub></a> </td> <td bgcolor="#f0f0ff"><span typeof="mw:File"><a href="/wiki/File:5-cube_t1234.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/5-cube_t1234.svg/80px-5-cube_t1234.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/5-cube_t1234.svg/120px-5-cube_t1234.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b6/5-cube_t1234.svg/160px-5-cube_t1234.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Runcicantitruncated_5-orthoplex" class="mw-redirect" title="Runcicantitruncated 5-orthoplex">t<sub>0,1,2,3</sub>β<sub>5</sub></a> </td> <td bgcolor="#f0f0ff"><span typeof="mw:File"><a href="/wiki/File:5-cube_t0234.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/5-cube_t0234.svg/80px-5-cube_t0234.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/5-cube_t0234.svg/120px-5-cube_t0234.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7d/5-cube_t0234.svg/160px-5-cube_t0234.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Stericantitruncated_5-orthoplex" class="mw-redirect" title="Stericantitruncated 5-orthoplex">t<sub>0,1,2,4</sub>β<sub>5</sub></a> </td> <td bgcolor="#f0fff0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t0134.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/5-cube_t0134.svg/80px-5-cube_t0134.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/5-cube_t0134.svg/120px-5-cube_t0134.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/5-cube_t0134.svg/160px-5-cube_t0134.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Steriruncitruncated_5-cube" class="mw-redirect" title="Steriruncitruncated 5-cube">t<sub>0,1,3,4</sub>γ<sub>5</sub></a> </td> <td bgcolor="#fff0f0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t0124.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/5-cube_t0124.svg/80px-5-cube_t0124.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/5-cube_t0124.svg/120px-5-cube_t0124.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5c/5-cube_t0124.svg/160px-5-cube_t0124.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Stericantitruncated_5-cube" class="mw-redirect" title="Stericantitruncated 5-cube">t<sub>0,1,2,4</sub>γ<sub>5</sub></a> </td> <td bgcolor="#fff0f0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t0123.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/5-cube_t0123.svg/80px-5-cube_t0123.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/5-cube_t0123.svg/120px-5-cube_t0123.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e7/5-cube_t0123.svg/160px-5-cube_t0123.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Runcicantitruncated_5-cube" class="mw-redirect" title="Runcicantitruncated 5-cube">t<sub>0,1,2,3</sub>γ<sub>5</sub></a> </td> <td bgcolor="#f0fff0"><span typeof="mw:File"><a href="/wiki/File:5-cube_t01234.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/5-cube_t01234.svg/80px-5-cube_t01234.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/5-cube_t01234.svg/120px-5-cube_t01234.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c6/5-cube_t01234.svg/160px-5-cube_t01234.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span><br /><a href="/wiki/Omnitruncated_5-cube" class="mw-redirect" title="Omnitruncated 5-cube">t<sub>0,1,2,3,4</sub>γ<sub>5</sub></a> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rectified_5-cubes&action=edit&section=12" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rectified_5-cubes&action=edit&section=13" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Harold_Scott_MacDonald_Coxeter" title="Harold Scott MacDonald Coxeter">H.S.M. Coxeter</a>: <ul><li>H.S.M. Coxeter, <i>Regular Polytopes</i>, 3rd Edition, Dover New York, 1973</li> <li><b>Kaleidoscopes: Selected Writings of H.S.M. Coxeter</b>, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, <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><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 22) H.S.M. Coxeter, <i>Regular and Semi Regular Polytopes I</i>, [Math. Zeit. 46 (1940) 380-407, MR 2,10]</li> <li>(Paper 23) H.S.M. Coxeter, <i>Regular and Semi-Regular Polytopes II</i>, [Math. Zeit. 188 (1985) 559-591]</li> <li>(Paper 24) H.S.M. Coxeter, <i>Regular and Semi-Regular Polytopes III</i>, [Math. Zeit. 200 (1988) 3-45]</li></ul></li></ul></li> <li><a href="/wiki/Norman_Johnson_(mathematician)" title="Norman Johnson (mathematician)">Norman Johnson</a> <i>Uniform Polytopes</i>, Manuscript (1991) <ul><li>N.W. Johnson: <i>The Theory of Uniform Polytopes and Honeycombs</i>, Ph.D.</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/polytera.htm">"5D uniform polytopes (polytera)"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=5D+uniform+polytopes+%28polytera%29&rft.aulast=Klitzing&rft.aufirst=Richard&rft_id=https%3A%2F%2Fbendwavy.org%2Fklitzing%2Fdimensions%2Fpolytera.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARectified+5-cubes" class="Z3988"></span> o3x3o3o4o - rin, o3o3x3o4o - nit</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rectified_5-cubes&action=edit&section=14" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070310205351/http://members.cox.net/hedrondude/topes.htm">Polytopes of Various Dimensions</a></li> <li><a rel="nofollow" class="external text" href="http://tetraspace.alkaline.org/glossary.htm">Multi-dimensional Glossary</a></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 ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style 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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"><i>A</i><sub><i>n</i></sub></a> </td> <td style="background:gainsboro;"><a href="/wiki/Simple_Lie_group#B_series" title="Simple Lie group"><i>B</i><sub><i>n</i></sub></a> </td> <td style="background:gainsboro;"><span style="background-color: #f0f0e0; color:;"><i>I</i><sub>2</sub>(p)</span> / <a href="/wiki/Simple_Lie_group#D_series" title="Simple Lie group"><i>D</i><sub><i>n</i></sub></a> </td> <td style="background:gainsboro;"><span style="background-color: #f0e0e0; color:;"><a href="/wiki/E6_(mathematics)" title="E6 (mathematics)"><i>E</i><sub>6</sub></a> / <a href="/wiki/E7_(mathematics)" title="E7 (mathematics)"><i>E</i><sub>7</sub></a> / <a href="/wiki/E8_(mathematics)" title="E8 (mathematics)"><i>E</i><sub>8</sub></a></span> / <span style="background-color: #e0f0e0; color:;"><a href="/wiki/F4_(mathematics)" title="F4 (mathematics)"><i>F</i><sub>4</sub></a></span> / <span style="background-color: #e0e0f0; color:;"><a href="/wiki/G2_(mathematics)" title="G2 (mathematics)"><i>G</i><sub>2</sub></a></span> </td> <td style="background:gainsboro;"><a href="/wiki/H4_(mathematics)" class="mw-redirect" title="H4 (mathematics)">H<sub>n</sub></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">1<sub>22</sub></a> • <a href="/wiki/2_21_polytope" title="2 21 polytope">2<sub>21</sub></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 href="/wiki/1_32_polytope" title="1 32 polytope">1<sub>32</sub></a> • <a href="/wiki/2_31_polytope" title="2 31 polytope">2<sub>31</sub></a> • <a href="/wiki/3_21_polytope" title="3 21 polytope">3<sub>21</sub></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">1<sub>42</sub></a> • <a href="/wiki/2_41_polytope" title="2 41 polytope">2<sub>41</sub></a> • <a href="/wiki/4_21_polytope" title="4 21 polytope">4<sub>21</sub></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 <i>n</i>-<a href="/wiki/Polytope" title="Polytope">polytope</a> </th> <td style="background:whitesmoke;"><i>n</i>-<a href="/wiki/Simplex" title="Simplex">simplex</a> </td> <td style="background:whitesmoke;"><i>n</i>-<a href="/wiki/Cross-polytope" title="Cross-polytope">orthoplex</a> • <i>n</i>-<a href="/wiki/Hypercube" title="Hypercube">cube</a> </td> <td style="background:whitesmoke;"><i>n</i>-<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">1<sub>k2</sub></a> • <a href="/wiki/Uniform_2_k1_polytope" title="Uniform 2 k1 polytope">2<sub>k1</sub></a> • <a href="/wiki/Uniform_k_21_polytope" title="Uniform k 21 polytope">k<sub>21</sub></a> </td> <td style="background:whitesmoke;"><i>n</i>-<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&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" 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