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Available in 19 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-19" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">19 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Tetr%C3%A0edre_triakis" title="Tetràedre triakis – Catalan" lang="ca" hreflang="ca" data-title="Tetràedre triakis" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Triakistetraeder" title="Triakistetraeder – German" lang="de" hreflang="de" data-title="Triakistetraeder" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A4%CF%81%CE%B9%CE%AC%CE%BA%CE%B9%CF%82_%CF%84%CE%B5%CF%84%CF%81%CE%AC%CE%B5%CE%B4%CF%81%CE%BF" title="Τριάκις τετράεδρο – Greek" lang="el" hreflang="el" data-title="Τριάκις τετράεδρο" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Triaquistetraedro" title="Triaquistetraedro – Spanish" lang="es" hreflang="es" data-title="Triaquistetraedro" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Trilateropiramidigita_kvaredro" title="Trilateropiramidigita kvaredro – Esperanto" lang="eo" hreflang="eo" data-title="Trilateropiramidigita kvaredro" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Triakistetraedro" title="Triakistetraedro – Basque" lang="eu" hreflang="eu" data-title="Triakistetraedro" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AF%D9%88%D8%A7%D8%B2%D8%AF%D9%87%E2%80%8C%D9%85%D8%AB%D9%84%D8%AB_%D9%88%D8%AC%D9%87%DB%8C" title="دوازده‌مثلث وجهی – Persian" lang="fa" hreflang="fa" data-title="دوازده‌مثلث وجهی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Triakit%C3%A9tra%C3%A8dre" title="Triakitétraèdre – French" lang="fr" hreflang="fr" data-title="Triakitétraèdre" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%82%BC%EB%B0%A9%EC%82%AC%EB%A9%B4%EC%B2%B4" title="삼방사면체 – Korean" lang="ko" hreflang="ko" data-title="삼방사면체" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Triacistetraedro" title="Triacistetraedro – Italian" lang="it" hreflang="it" data-title="Triacistetraedro" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%B8%89%E6%96%B9%E5%9B%9B%E9%9D%A2%E4%BD%93" title="三方四面体 – Japanese" lang="ja" hreflang="ja" data-title="三方四面体" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Triakistetraeder" title="Triakistetraeder – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Triakistetraeder" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Czworo%C5%9Bcian_potr%C3%B3jny" title="Czworościan potrójny – Polish" lang="pl" hreflang="pl" data-title="Czworościan potrójny" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Tetraedro_triakis" title="Tetraedro triakis – Portuguese" lang="pt" hreflang="pt" data-title="Tetraedro triakis" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Tetraedru_triakis" title="Tetraedru triakis – Romanian" lang="ro" hreflang="ro" data-title="Tetraedru triakis" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D0%B0%D0%BA%D0%B8%D1%81%D1%82%D0%B5%D1%82%D1%80%D0%B0%D1%8D%D0%B4%D1%80" title="Триакистетраэдр – Russian" lang="ru" hreflang="ru" data-title="Триакистетраэдр" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Triakisni_tetraeder" title="Triakisni tetraeder – Slovenian" lang="sl" hreflang="sl" data-title="Triakisni tetraeder" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D0%B0%D0%BA%D1%96%D1%81%D1%82%D0%B5%D1%82%D1%80%D0%B0%D0%B5%D0%B4%D1%80" title="Триакістетраедр – Ukrainian" lang="uk" 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</div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" 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tetrahedron </th></tr> <tr> <td style="text-align:center;" colspan="2"><span typeof="mw:File"><a href="/wiki/File:Triakistetrahedron.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Triakistetrahedron.jpg/280px-Triakistetrahedron.jpg" decoding="async" width="280" height="315" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Triakistetrahedron.jpg/420px-Triakistetrahedron.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/Triakistetrahedron.jpg/560px-Triakistetrahedron.jpg 2x" data-file-width="681" data-file-height="766" /></a></span><br /><a href="/wiki/File:Triakistetrahedron.gif" title="File:Triakistetrahedron.gif">(Click here for rotating model)</a> </td></tr> <tr> <td style="background-color:#e7dcc3;">Type</td> <td><a href="/wiki/Catalan_solid" title="Catalan solid">Catalan solid</a> </td></tr> <tr> <td style="background-color:#e7dcc3;"><a href="/wiki/Coxeter%E2%80%93Dynkin_diagram" title="Coxeter–Dynkin diagram">Coxeter diagram</a></td> <td><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/9/9b/CDel_node_f1.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/9/9b/CDel_node_f1.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;"><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">Conway notation</a></td> <td>kT </td></tr> <tr> <td style="background-color:#e7dcc3;"><a href="/wiki/Face_configuration" class="mw-redirect" title="Face configuration">Face type</a></td> <td>V3.6.6<figure class="mw-halign-right" typeof="mw:File"><a href="/wiki/File:DU02_facets.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/DU02_facets.png/60px-DU02_facets.png" decoding="async" width="60" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/DU02_facets.png/90px-DU02_facets.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a3/DU02_facets.png/120px-DU02_facets.png 2x" data-file-width="1189" data-file-height="472" /></a><figcaption></figcaption></figure><br />isosceles triangle </td></tr> <tr> <td style="background-color:#e7dcc3;">Faces</td> <td>12 </td></tr> <tr> <td style="background-color:#e7dcc3;">Edges</td> <td>18 </td></tr> <tr> <td style="background-color:#e7dcc3;">Vertices</td> <td>8 </td></tr> <tr> <td style="background-color:#e7dcc3;">Vertices by type</td> <td>4{3}+4{6} </td></tr> <tr> <td style="background-color:#e7dcc3;"><a href="/wiki/List_of_spherical_symmetry_groups" title="List of spherical symmetry groups">Symmetry group</a></td> <td><a href="/wiki/Tetrahedral_symmetry" title="Tetrahedral symmetry">T<sub>d</sub></a>, A<sub>3</sub>, [3,3], (*332) </td></tr> <tr> <td style="background-color:#e7dcc3;"><a href="/wiki/Point_groups_in_three_dimensions#Rotation_groups" title="Point groups in three dimensions">Rotation group</a></td> <td>T, [3,3]<sup>+</sup>, (332) </td></tr> <tr> <td style="background-color:#e7dcc3;"><a href="/wiki/Dihedral_angle" title="Dihedral angle">Dihedral angle</a></td> <td>129°31′16″<br />arccos(−<style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">7</span><span class="sr-only">/</span><span class="den">11</span></span>⁠</span>) </td></tr> <tr> <td style="background-color:#e7dcc3;">Properties</td> <td>convex, <a href="/wiki/Face-transitive" class="mw-redirect" title="Face-transitive">face-transitive</a> </td></tr> <tr> <td style="vertical-align:top;text-align:center;"><span typeof="mw:File"><a href="/wiki/File:Truncated_tetrahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Truncated_tetrahedron.png/100px-Truncated_tetrahedron.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Truncated_tetrahedron.png/150px-Truncated_tetrahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/75/Truncated_tetrahedron.png/200px-Truncated_tetrahedron.png 2x" data-file-width="1000" data-file-height="1000" /></a></span><br /><a href="/wiki/Truncated_tetrahedron" title="Truncated tetrahedron">Truncated tetrahedron</a><br />(<a href="/wiki/Dual_polyhedron" title="Dual polyhedron">dual polyhedron</a>) </td> <td style="vertical-align:top;text-align:center;"><span typeof="mw:File"><a href="/wiki/File:Triakis_tetrahedron_net.svg" class="mw-file-description" title="Triakis tetrahedron Net"><img alt="Triakis tetrahedron Net" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Triakis_tetrahedron_net.svg/100px-Triakis_tetrahedron_net.svg.png" decoding="async" width="100" height="59" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Triakis_tetrahedron_net.svg/150px-Triakis_tetrahedron_net.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Triakis_tetrahedron_net.svg/200px-Triakis_tetrahedron_net.svg.png 2x" data-file-width="1200" data-file-height="708" /></a></span><br /><a href="/wiki/Net_(polyhedron)" title="Net (polyhedron)">Net</a> </td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><span class="mw-3d-wrapper" data-label="3D"><a href="/wiki/File:Triakis_tetrahedron.stl" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Triakis_tetrahedron.stl/220px-Triakis_tetrahedron.stl.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Triakis_tetrahedron.stl/330px-Triakis_tetrahedron.stl.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Triakis_tetrahedron.stl/440px-Triakis_tetrahedron.stl.png 2x" data-file-width="5120" data-file-height="2880" /></a></span><figcaption>3D model of a triakis tetrahedron</figcaption></figure> <p>In <a href="/wiki/Geometry" title="Geometry">geometry</a>, a <b>triakis tetrahedron</b> (or <b>kistetrahedron</b><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>) is a <a href="/wiki/Catalan_solid" title="Catalan solid">Catalan solid</a> with 12 faces. Each Catalan solid is the dual of an <a href="/wiki/Archimedean_solid" title="Archimedean solid">Archimedean solid</a>. The dual of the triakis tetrahedron is the <a href="/wiki/Truncated_tetrahedron" title="Truncated tetrahedron">truncated tetrahedron</a>. </p><p>The triakis tetrahedron can be seen as a <a href="/wiki/Tetrahedron" title="Tetrahedron">tetrahedron</a> with a <a href="/wiki/Triangular_pyramid" class="mw-redirect" title="Triangular pyramid">triangular pyramid</a> added to each face; that is, it is the <a href="/wiki/Kleetope" title="Kleetope">Kleetope</a> of the tetrahedron. It is very similar to the net for the <a href="/wiki/5-cell" title="5-cell">5-cell</a>, as the net for a tetrahedron is a triangle with other triangles added to each edge, the net for the 5-cell a tetrahedron with pyramids attached to each face. This interpretation is expressed in the name. </p><p>The length of the shorter edges is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">3</span><span class="sr-only">/</span><span class="den">5</span></span>⁠</span> that of the longer edges.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The area, A, and volume, V, of the triakis tetrahedron, with shorter edge length "a", is equal to </p><p>A = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">5</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span><span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">11</span></span> V = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">25</span><span class="sr-only">/</span><span class="den">36</span></span>⁠</span><span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">2</span></span>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Cartesian_coordinates">Cartesian coordinates</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Triakis_tetrahedron&action=edit&section=1" title="Edit section: Cartesian coordinates"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Cartesian_coordinates" class="mw-redirect" title="Cartesian coordinates">Cartesian coordinates</a> for the 8 vertices of a triakis tetrahedron centered at the origin, are the points (±<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">5</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span>, ±<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">5</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span>, ±<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">5</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span>) with an even number of minus signs, along with the points (±1, ±1, ±1) with an odd number of minus signs: </p> <ul><li>(<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">5</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span>, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">5</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span>, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">5</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span>), (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">5</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span>, −<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">5</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span>, −<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">5</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span>), (−<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">5</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span>, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">5</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span>, −<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">5</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span>), (−<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">5</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span>, −<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">5</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span>, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">5</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span>)</li> <li>(−1, 1, 1), (1, −1, 1), (1, 1, −1), (−1, −1, −1)</li></ul> <p>The length of the shorter edges of this triakis tetrahedron equals 2<span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">2</span></span>. The faces are isosceles triangles with one obtuse and two acute angles. The obtuse angle equals arccos(–<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">7</span><span class="sr-only">/</span><span class="den">18</span></span>⁠</span>) ≈ <span class="nowrap"><span data-sort-value="7002112885380476160♠"></span>112.885<span style="margin-left:.25em;">380</span><span style="margin-left:.25em;">476</span><span style="margin-left:.25em;">16</span></span>° and the acute ones equal arccos(<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">5</span><span class="sr-only">/</span><span class="den">6</span></span>⁠</span>) ≈ <span class="nowrap"><span data-sort-value="7001335573097619200♠"></span>33.557<span style="margin-left:.25em;">309</span><span style="margin-left:.25em;">761</span><span style="margin-left:.25em;">92</span></span>°. </p> <div class="mw-heading mw-heading2"><h2 id="Tetartoid_symmetry">Tetartoid symmetry</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Triakis_tetrahedron&action=edit&section=2" title="Edit section: Tetartoid symmetry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The triakis tetrahedron can be made as a degenerate limit of a <a href="/wiki/Tetartoid" class="mw-redirect" title="Tetartoid">tetartoid</a>: </p> <table class="wikitable"> <caption>Example tetartoid variations </caption> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/File:Dodecahedron.png" class="mw-file-description" title="Tetartoid 0% (Regular Dodecahedron)"><img alt="Tetartoid 0% (Regular Dodecahedron)" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Dodecahedron.png/140px-Dodecahedron.png" decoding="async" width="140" height="135" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Dodecahedron.png/210px-Dodecahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/Dodecahedron.png/280px-Dodecahedron.png 2x" data-file-width="984" data-file-height="951" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Tetartoid-010.png" class="mw-file-description" title="Tetartoid 10%"><img alt="Tetartoid 10%" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Tetartoid-010.png/150px-Tetartoid-010.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Tetartoid-010.png/225px-Tetartoid-010.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Tetartoid-010.png/300px-Tetartoid-010.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Tetartoid-020.png" class="mw-file-description" title="Tetartoid 20%"><img alt="Tetartoid 20%" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Tetartoid-020.png/150px-Tetartoid-020.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Tetartoid-020.png/225px-Tetartoid-020.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/90/Tetartoid-020.png/300px-Tetartoid-020.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Tetartoid-040.png" class="mw-file-description" title="Tetartoid 30%"><img alt="Tetartoid 30%" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Tetartoid-040.png/150px-Tetartoid-040.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Tetartoid-040.png/225px-Tetartoid-040.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Tetartoid-040.png/300px-Tetartoid-040.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Tetartoid-060.png" class="mw-file-description" title="Tetartoid 60%"><img alt="Tetartoid 60%" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Tetartoid-060.png/150px-Tetartoid-060.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Tetartoid-060.png/225px-Tetartoid-060.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/31/Tetartoid-060.png/300px-Tetartoid-060.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Tetartoid-080.png" class="mw-file-description" title="Tetartoid 80%"><img alt="Tetartoid 80%" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Tetartoid-080.png/150px-Tetartoid-080.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Tetartoid-080.png/225px-Tetartoid-080.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Tetartoid-080.png/300px-Tetartoid-080.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Tetartoid-095.png" class="mw-file-description" title="Tetartoid 95%"><img alt="Tetartoid 95%" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Tetartoid-095.png/150px-Tetartoid-095.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Tetartoid-095.png/225px-Tetartoid-095.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Tetartoid-095.png/300px-Tetartoid-095.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Triakistetrahedron.jpg" class="mw-file-description" title="Tetartoid 100% (Triakis Tetrahedron)"><img alt="Tetartoid 100% (Triakis Tetrahedron)" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Triakistetrahedron.jpg/100px-Triakistetrahedron.jpg" decoding="async" width="100" height="112" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Triakistetrahedron.jpg/150px-Triakistetrahedron.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/Triakistetrahedron.jpg/200px-Triakistetrahedron.jpg 2x" data-file-width="681" data-file-height="766" /></a></span> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Orthogonal_projections">Orthogonal projections</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Triakis_tetrahedron&action=edit&section=3" title="Edit section: Orthogonal projections"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable collapsible open"> <tbody><tr> <th colspan="5"><a href="/wiki/Orthogonal_projection" class="mw-redirect" title="Orthogonal projection">Orthogonal projections</a> (graphs) </th></tr> <tr> <th>Centered by </th> <th>Short edge </th> <th>Face </th> <th>Vertex </th> <th>Long edge </th></tr> <tr> <th>Triakis<br />tetrahedron </th> <td><span typeof="mw:File"><a href="/wiki/File:Dual_tetrahedron_t01_ae.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Dual_tetrahedron_t01_ae.png/100px-Dual_tetrahedron_t01_ae.png" decoding="async" width="100" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Dual_tetrahedron_t01_ae.png/150px-Dual_tetrahedron_t01_ae.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Dual_tetrahedron_t01_ae.png/200px-Dual_tetrahedron_t01_ae.png 2x" data-file-width="456" data-file-height="567" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dual_tetrahedron_t01_af36.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Dual_tetrahedron_t01_af36.png/100px-Dual_tetrahedron_t01_af36.png" decoding="async" width="100" height="103" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Dual_tetrahedron_t01_af36.png/150px-Dual_tetrahedron_t01_af36.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Dual_tetrahedron_t01_af36.png/200px-Dual_tetrahedron_t01_af36.png 2x" data-file-width="483" data-file-height="496" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dual_tetrahedron_t01_A2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Dual_tetrahedron_t01_A2.png/100px-Dual_tetrahedron_t01_A2.png" decoding="async" width="100" height="102" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Dual_tetrahedron_t01_A2.png/150px-Dual_tetrahedron_t01_A2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Dual_tetrahedron_t01_A2.png/200px-Dual_tetrahedron_t01_A2.png 2x" data-file-width="535" data-file-height="546" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dual_tetrahedron_t01.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/48/Dual_tetrahedron_t01.png/100px-Dual_tetrahedron_t01.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/48/Dual_tetrahedron_t01.png/150px-Dual_tetrahedron_t01.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/48/Dual_tetrahedron_t01.png/200px-Dual_tetrahedron_t01.png 2x" data-file-width="399" data-file-height="398" /></a></span> </td></tr> <tr> <th><small>(Dual)</small><br /><a href="/wiki/Truncated_tetrahedron" title="Truncated tetrahedron">Truncated<br />tetrahedron</a> </th> <td><span typeof="mw:File"><a href="/wiki/File:Tetrahedron_t01_ae.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Tetrahedron_t01_ae.png/100px-Tetrahedron_t01_ae.png" decoding="async" width="100" height="94" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Tetrahedron_t01_ae.png/150px-Tetrahedron_t01_ae.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Tetrahedron_t01_ae.png/200px-Tetrahedron_t01_ae.png 2x" data-file-width="894" data-file-height="839" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Tetrahedron_t01_af36.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Tetrahedron_t01_af36.png/100px-Tetrahedron_t01_af36.png" decoding="async" width="100" height="83" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Tetrahedron_t01_af36.png/150px-Tetrahedron_t01_af36.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/90/Tetrahedron_t01_af36.png/200px-Tetrahedron_t01_af36.png 2x" data-file-width="867" data-file-height="721" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:3-simplex_t01_A2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/3-simplex_t01_A2.svg/100px-3-simplex_t01_A2.svg.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/3-simplex_t01_A2.svg/150px-3-simplex_t01_A2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9f/3-simplex_t01_A2.svg/200px-3-simplex_t01_A2.svg.png 2x" data-file-width="1600" data-file-height="1600" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:3-simplex_t01.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/3-simplex_t01.svg/100px-3-simplex_t01.svg.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/3-simplex_t01.svg/150px-3-simplex_t01.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/54/3-simplex_t01.svg/200px-3-simplex_t01.svg.png 2x" data-file-width="3200" data-file-height="3200" /></a></span> </td></tr> <tr> <th>Projective<br />symmetry </th> <th colspan="2">[1] </th> <th>[3] </th> <th>[4] </th></tr></tbody></table> <table class="wikitable collapsible collapsed"> <tbody><tr> <th colspan="5">Orthogonal projections (solids) </th></tr> <tr> <th>Triakis<br />tetrahedron </th> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_4a_dual_from_redyellow.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Polyhedron_truncated_4a_dual_from_redyellow.png/100px-Polyhedron_truncated_4a_dual_from_redyellow.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Polyhedron_truncated_4a_dual_from_redyellow.png/150px-Polyhedron_truncated_4a_dual_from_redyellow.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/02/Polyhedron_truncated_4a_dual_from_redyellow.png/200px-Polyhedron_truncated_4a_dual_from_redyellow.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_4a_dual_from_blue.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Polyhedron_truncated_4a_dual_from_blue.png/100px-Polyhedron_truncated_4a_dual_from_blue.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Polyhedron_truncated_4a_dual_from_blue.png/150px-Polyhedron_truncated_4a_dual_from_blue.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Polyhedron_truncated_4a_dual_from_blue.png/200px-Polyhedron_truncated_4a_dual_from_blue.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_4a_dual_from_red.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Polyhedron_truncated_4a_dual_from_red.png/100px-Polyhedron_truncated_4a_dual_from_red.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Polyhedron_truncated_4a_dual_from_red.png/150px-Polyhedron_truncated_4a_dual_from_red.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/90/Polyhedron_truncated_4a_dual_from_red.png/200px-Polyhedron_truncated_4a_dual_from_red.png 2x" data-file-width="2430" data-file-height="2430" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_4a_dual_from_yellow.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Polyhedron_truncated_4a_dual_from_yellow.png/100px-Polyhedron_truncated_4a_dual_from_yellow.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Polyhedron_truncated_4a_dual_from_yellow.png/150px-Polyhedron_truncated_4a_dual_from_yellow.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Polyhedron_truncated_4a_dual_from_yellow.png/200px-Polyhedron_truncated_4a_dual_from_yellow.png 2x" data-file-width="2430" data-file-height="2430" /></a></span> </td></tr> <tr> <th><a href="/wiki/Dual_compound" class="mw-redirect" title="Dual compound">Dual<br />compound</a> </th> <td><span typeof="mw:File"><a href="/wiki/File:Dual_compound_truncated_4a_from_1-fold.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Dual_compound_truncated_4a_from_1-fold.png/100px-Dual_compound_truncated_4a_from_1-fold.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Dual_compound_truncated_4a_from_1-fold.png/150px-Dual_compound_truncated_4a_from_1-fold.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/01/Dual_compound_truncated_4a_from_1-fold.png/200px-Dual_compound_truncated_4a_from_1-fold.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dual_compound_truncated_4a_from_2-fold.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Dual_compound_truncated_4a_from_2-fold.png/100px-Dual_compound_truncated_4a_from_2-fold.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Dual_compound_truncated_4a_from_2-fold.png/150px-Dual_compound_truncated_4a_from_2-fold.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Dual_compound_truncated_4a_from_2-fold.png/200px-Dual_compound_truncated_4a_from_2-fold.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dual_compound_truncated_4_from_hexagon.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Dual_compound_truncated_4_from_hexagon.png/100px-Dual_compound_truncated_4_from_hexagon.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Dual_compound_truncated_4_from_hexagon.png/150px-Dual_compound_truncated_4_from_hexagon.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Dual_compound_truncated_4_from_hexagon.png/200px-Dual_compound_truncated_4_from_hexagon.png 2x" data-file-width="2430" data-file-height="2430" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dual_compound_truncated_4_from_triangle.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a8/Dual_compound_truncated_4_from_triangle.png/100px-Dual_compound_truncated_4_from_triangle.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a8/Dual_compound_truncated_4_from_triangle.png/150px-Dual_compound_truncated_4_from_triangle.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a8/Dual_compound_truncated_4_from_triangle.png/200px-Dual_compound_truncated_4_from_triangle.png 2x" data-file-width="2430" data-file-height="2430" /></a></span> </td></tr> <tr> <th><small>(Dual)</small><br />Truncated<br />tetrahedron </th> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_4a_from_redyellow.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Polyhedron_truncated_4a_from_redyellow.png/100px-Polyhedron_truncated_4a_from_redyellow.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Polyhedron_truncated_4a_from_redyellow.png/150px-Polyhedron_truncated_4a_from_redyellow.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Polyhedron_truncated_4a_from_redyellow.png/200px-Polyhedron_truncated_4a_from_redyellow.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_4a_from_blue.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Polyhedron_truncated_4a_from_blue.png/100px-Polyhedron_truncated_4a_from_blue.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Polyhedron_truncated_4a_from_blue.png/150px-Polyhedron_truncated_4a_from_blue.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Polyhedron_truncated_4a_from_blue.png/200px-Polyhedron_truncated_4a_from_blue.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_4a_from_red.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Polyhedron_truncated_4a_from_red.png/100px-Polyhedron_truncated_4a_from_red.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Polyhedron_truncated_4a_from_red.png/150px-Polyhedron_truncated_4a_from_red.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Polyhedron_truncated_4a_from_red.png/200px-Polyhedron_truncated_4a_from_red.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_4a_from_yellow.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Polyhedron_truncated_4a_from_yellow.png/100px-Polyhedron_truncated_4a_from_yellow.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Polyhedron_truncated_4a_from_yellow.png/150px-Polyhedron_truncated_4a_from_yellow.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Polyhedron_truncated_4a_from_yellow.png/200px-Polyhedron_truncated_4a_from_yellow.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td></tr> <tr> <th>Projective<br />symmetry </th> <th>[1] </th> <th>[2] </th> <th colspan="2">[3] </th></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Variations">Variations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Triakis_tetrahedron&action=edit&section=4" title="Edit section: Variations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A triakis tetrahedron with equilateral triangle faces represents a <a href="/wiki/Polyhedral_net" class="mw-redirect" title="Polyhedral net">net</a> of the four-dimensional regular polytope known as the <a href="/wiki/5-cell" title="5-cell">5-cell</a>. </p> <dl><dd><span typeof="mw:File"><a href="/wiki/File:5-cell_net.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/5-cell_net.png/160px-5-cell_net.png" decoding="async" width="160" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/5-cell_net.png/240px-5-cell_net.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cf/5-cell_net.png/320px-5-cell_net.png 2x" data-file-width="1172" data-file-height="1097" /></a></span></dd></dl> <p>If the triangles are right-angled isosceles, the faces will be coplanar and form a cubic volume. This can be seen by adding the 6 edges of <a href="/wiki/Disphenoid" title="Disphenoid">tetrahedron</a> inside of a <a href="/wiki/Cube" title="Cube">cube</a>. </p> <dl><dd><span typeof="mw:File"><a href="/wiki/File:Rhombic_disphenoid.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Rhombic_disphenoid.png/240px-Rhombic_disphenoid.png" decoding="async" width="240" height="234" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Rhombic_disphenoid.png/360px-Rhombic_disphenoid.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/81/Rhombic_disphenoid.png/480px-Rhombic_disphenoid.png 2x" data-file-width="815" data-file-height="796" /></a></span></dd></dl> <p>In <a href="/wiki/Modular_origami" title="Modular origami">modular origami</a>, this is the result to connecting six <a href="/wiki/Sonobe" title="Sonobe">Sonobe</a> modules to form a triakis tetrahedron. </p> <div class="mw-heading mw-heading2"><h2 id="Stellations">Stellations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Triakis_tetrahedron&action=edit&section=5" title="Edit section: Stellations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><span typeof="mw:File"><a href="/wiki/File:Stellation_of_triakis_tetrahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Stellation_of_triakis_tetrahedron.png/160px-Stellation_of_triakis_tetrahedron.png" decoding="async" width="160" height="160" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Stellation_of_triakis_tetrahedron.png/240px-Stellation_of_triakis_tetrahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Stellation_of_triakis_tetrahedron.png/320px-Stellation_of_triakis_tetrahedron.png 2x" data-file-width="1000" data-file-height="1000" /></a></span></dd></dl> <p>This chiral figure is one of thirteen <a href="/wiki/Stellation" title="Stellation">stellations</a> allowed by <a href="/wiki/The_Fifty-Nine_Icosahedra#Miller's_rules" title="The Fifty-Nine Icosahedra">Miller's rules</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Related_polyhedra">Related polyhedra</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Triakis_tetrahedron&action=edit&section=6" title="Edit section: Related polyhedra"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Spherical_triakis_tetrahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Spherical_triakis_tetrahedron.png/160px-Spherical_triakis_tetrahedron.png" decoding="async" width="160" height="158" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Spherical_triakis_tetrahedron.png/240px-Spherical_triakis_tetrahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Spherical_triakis_tetrahedron.png/320px-Spherical_triakis_tetrahedron.png 2x" data-file-width="604" data-file-height="596" /></a><figcaption>Spherical triakis tetrahedron</figcaption></figure> <p>The triakis tetrahedron is a part of a sequence of polyhedra and tilings, extending into the hyperbolic plane. These <a href="/wiki/Face-transitive" class="mw-redirect" title="Face-transitive">face-transitive</a> figures have (*<i>n</i>32) reflectional <a href="/wiki/Orbifold_notation" title="Orbifold notation">symmetry</a>. </p> <table class="wikitable mw-collapsible mw-collapsed"> <tbody><tr> <th colspan="12">*<i>n</i>32 symmetry mutation of truncated tilings: t{<i>n</i>,3} <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 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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 data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini" style="float:right;"><ul class="navbar-brackets"><li class="nv-view"><a href="/wiki/Template:Truncated_figure1_table" title="Template:Truncated figure1 table"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Truncated_figure1_table" title="Template talk:Truncated figure1 table"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Truncated_figure1_table" title="Special:EditPage/Template:Truncated figure1 table"><abbr title="Edit this template">e</abbr></a></li></ul></div> </th></tr> <tr> <th rowspan="2">Symmetry<br />*<i>n</i>32<br />[n,3] </th> <th colspan="4"><a href="/wiki/List_of_spherical_symmetry_groups" title="List of spherical symmetry groups">Spherical</a> </th> <th><a href="/wiki/List_of_planar_symmetry_groups" title="List of planar symmetry groups">Euclid.</a> </th> <th colspan="2">Compact hyperb. </th> <th>Paraco. </th> <th colspan="3">Noncompact hyperbolic </th></tr> <tr> <th>*232<br />[2,3] </th> <th>*332<br />[3,3] </th> <th>*432<br />[4,3] </th> <th>*532<br />[5,3] </th> <th>*632<br />[6,3] </th> <th>*732<br />[7,3] </th> <th>*832<br />[8,3]... </th> <th>*∞32<br />[∞,3] </th> <th>[12i,3] </th> <th>[9i,3] </th> <th>[6i,3] </th></tr> <tr style="text-align:center;"> <th>Truncated<br />figures </th> <td><span typeof="mw:File"><a href="/wiki/File:Spherical_triangular_prism.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Spherical_triangular_prism.svg/50px-Spherical_triangular_prism.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Spherical_triangular_prism.svg/75px-Spherical_triangular_prism.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Spherical_triangular_prism.svg/100px-Spherical_triangular_prism.svg.png 2x" data-file-width="577" data-file-height="577" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_tiling_332-t01-1-.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Uniform_tiling_332-t01-1-.png/50px-Uniform_tiling_332-t01-1-.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Uniform_tiling_332-t01-1-.png/75px-Uniform_tiling_332-t01-1-.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Uniform_tiling_332-t01-1-.png/100px-Uniform_tiling_332-t01-1-.png 2x" data-file-width="812" data-file-height="817" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_tiling_432-t01.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Uniform_tiling_432-t01.png/50px-Uniform_tiling_432-t01.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Uniform_tiling_432-t01.png/75px-Uniform_tiling_432-t01.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Uniform_tiling_432-t01.png/100px-Uniform_tiling_432-t01.png 2x" data-file-width="820" data-file-height="821" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_tiling_532-t01.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Uniform_tiling_532-t01.png/50px-Uniform_tiling_532-t01.png" decoding="async" width="50" height="51" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Uniform_tiling_532-t01.png/75px-Uniform_tiling_532-t01.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Uniform_tiling_532-t01.png/100px-Uniform_tiling_532-t01.png 2x" data-file-width="813" data-file-height="827" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_tiling_63-t01.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Uniform_tiling_63-t01.svg/50px-Uniform_tiling_63-t01.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Uniform_tiling_63-t01.svg/75px-Uniform_tiling_63-t01.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Uniform_tiling_63-t01.svg/100px-Uniform_tiling_63-t01.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Truncated_heptagonal_tiling.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Truncated_heptagonal_tiling.svg/50px-Truncated_heptagonal_tiling.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Truncated_heptagonal_tiling.svg/75px-Truncated_heptagonal_tiling.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Truncated_heptagonal_tiling.svg/100px-Truncated_heptagonal_tiling.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:H2-8-3-trunc-dual.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/H2-8-3-trunc-dual.svg/50px-H2-8-3-trunc-dual.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/H2-8-3-trunc-dual.svg/75px-H2-8-3-trunc-dual.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9d/H2-8-3-trunc-dual.svg/100px-H2-8-3-trunc-dual.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:H2_tiling_23i-3.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/H2_tiling_23i-3.png/50px-H2_tiling_23i-3.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/H2_tiling_23i-3.png/75px-H2_tiling_23i-3.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e0/H2_tiling_23i-3.png/100px-H2_tiling_23i-3.png 2x" data-file-width="2520" data-file-height="2520" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:H2_tiling_23j12-3.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/H2_tiling_23j12-3.png/50px-H2_tiling_23j12-3.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/H2_tiling_23j12-3.png/75px-H2_tiling_23j12-3.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6b/H2_tiling_23j12-3.png/100px-H2_tiling_23j12-3.png 2x" data-file-width="2520" data-file-height="2520" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:H2_tiling_23j9-3.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/H2_tiling_23j9-3.png/50px-H2_tiling_23j9-3.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/H2_tiling_23j9-3.png/75px-H2_tiling_23j9-3.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/H2_tiling_23j9-3.png/100px-H2_tiling_23j9-3.png 2x" data-file-width="2520" data-file-height="2520" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:H2_tiling_23j6-3.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/H2_tiling_23j6-3.png/50px-H2_tiling_23j6-3.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/H2_tiling_23j6-3.png/75px-H2_tiling_23j6-3.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ea/H2_tiling_23j6-3.png/100px-H2_tiling_23j6-3.png 2x" data-file-width="2520" data-file-height="2520" /></a></span> </td></tr> <tr> <th><a href="/wiki/Schl%C3%A4fli_symbol" title="Schläfli symbol">Symbol</a> </th> <th><a href="/wiki/Triangular_prism" title="Triangular prism">t{2,3}</a> </th> <th><a href="/wiki/Truncated_tetrahedron" title="Truncated tetrahedron">t{3,3}</a> </th> <th><a href="/wiki/Truncated_cube" title="Truncated cube">t{4,3}</a> </th> <th><a href="/wiki/Truncated_dodecahedron" title="Truncated dodecahedron">t{5,3}</a> </th> <th><a href="/wiki/Truncated_hexagonal_tiling" title="Truncated hexagonal tiling">t{6,3}</a> </th> <th><a href="/wiki/Truncated_heptagonal_tiling" title="Truncated heptagonal tiling">t{7,3}</a> </th> <th><a href="/wiki/Truncated_octagonal_tiling" title="Truncated octagonal tiling">t{8,3}</a> </th> <th><a href="/wiki/Truncated_order-3_apeirogonal_tiling" title="Truncated order-3 apeirogonal tiling">t{∞,3}</a> </th> <th>t{12i,3} </th> <th>t{9i,3} </th> <th>t{6i,3} </th></tr> <tr style="text-align:center;vertical-align:bottom;"> <th>Triakis<br />figures </th> <td><span typeof="mw:File"><a href="/wiki/File:Spherical_trigonal_bipyramid.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Spherical_trigonal_bipyramid.svg/50px-Spherical_trigonal_bipyramid.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Spherical_trigonal_bipyramid.svg/75px-Spherical_trigonal_bipyramid.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/75/Spherical_trigonal_bipyramid.svg/100px-Spherical_trigonal_bipyramid.svg.png 2x" data-file-width="577" data-file-height="577" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Spherical_triakis_tetrahedron.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Spherical_triakis_tetrahedron.svg/50px-Spherical_triakis_tetrahedron.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Spherical_triakis_tetrahedron.svg/75px-Spherical_triakis_tetrahedron.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Spherical_triakis_tetrahedron.svg/100px-Spherical_triakis_tetrahedron.svg.png 2x" data-file-width="577" data-file-height="577" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Spherical_triakis_octahedron.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Spherical_triakis_octahedron.svg/50px-Spherical_triakis_octahedron.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Spherical_triakis_octahedron.svg/75px-Spherical_triakis_octahedron.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/52/Spherical_triakis_octahedron.svg/100px-Spherical_triakis_octahedron.svg.png 2x" data-file-width="577" data-file-height="577" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Spherical_triakis_icosahedron.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Spherical_triakis_icosahedron.svg/50px-Spherical_triakis_icosahedron.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Spherical_triakis_icosahedron.svg/75px-Spherical_triakis_icosahedron.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Spherical_triakis_icosahedron.svg/100px-Spherical_triakis_icosahedron.svg.png 2x" data-file-width="577" data-file-height="577" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Tiling_Dual_Semiregular_V3-12-12_Triakis_Triangular.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Tiling_Dual_Semiregular_V3-12-12_Triakis_Triangular.svg/50px-Tiling_Dual_Semiregular_V3-12-12_Triakis_Triangular.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Tiling_Dual_Semiregular_V3-12-12_Triakis_Triangular.svg/75px-Tiling_Dual_Semiregular_V3-12-12_Triakis_Triangular.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Tiling_Dual_Semiregular_V3-12-12_Triakis_Triangular.svg/100px-Tiling_Dual_Semiregular_V3-12-12_Triakis_Triangular.svg.png 2x" data-file-width="400" data-file-height="400" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Order-7_triakis_triangular_tiling.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Order-7_triakis_triangular_tiling.svg/50px-Order-7_triakis_triangular_tiling.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Order-7_triakis_triangular_tiling.svg/75px-Order-7_triakis_triangular_tiling.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Order-7_triakis_triangular_tiling.svg/100px-Order-7_triakis_triangular_tiling.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:H2-8-3-kis-primal.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/H2-8-3-kis-primal.svg/50px-H2-8-3-kis-primal.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/H2-8-3-kis-primal.svg/75px-H2-8-3-kis-primal.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/H2-8-3-kis-primal.svg/100px-H2-8-3-kis-primal.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Ord-infin_triakis_triang_til.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Ord-infin_triakis_triang_til.png/50px-Ord-infin_triakis_triang_til.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Ord-infin_triakis_triang_til.png/75px-Ord-infin_triakis_triang_til.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Ord-infin_triakis_triang_til.png/100px-Ord-infin_triakis_triang_til.png 2x" data-file-width="512" data-file-height="512" /></a></span> </td> <td> </td> <td> </td> <td> </td></tr> <tr style="text-align:center;vertical-align:bottom;"> <th><a href="/wiki/Face_configuration" class="mw-redirect" title="Face configuration">Config.</a> </th> <td><a href="/wiki/Triangular_dipyramid" class="mw-redirect" title="Triangular dipyramid">V3.4.4</a> </td> <td><a class="mw-selflink selflink">V3.6.6</a> </td> <td><a href="/wiki/Triakis_octahedron" title="Triakis octahedron">V3.8.8</a> </td> <td><a href="/wiki/Triakis_icosahedron" title="Triakis icosahedron">V3.10.10</a> </td> <td><a href="/wiki/Triakis_triangular_tiling" class="mw-redirect" title="Triakis triangular tiling">V3.12.12</a> </td> <td><a href="/wiki/Truncated_heptagonal_tiling#Dual_tiling" title="Truncated heptagonal tiling">V3.14.14</a> </td> <td>V3.16.16 </td> <td>V3.∞.∞ </td> <td> </td> <td> </td> <td> </td></tr></tbody></table> <table class="wikitable mw-collapsible mw-collapsed"> <tbody><tr> <th colspan="8"><a href="/wiki/Uniform_polyhedron#.283_3_2.29_Td_Tetrahedral_symmetry" title="Uniform polyhedron">Family of uniform tetrahedral polyhedra</a> </th></tr> <tr style="text-align:center;"> <th colspan="7"><a href="/wiki/List_of_spherical_symmetry_groups" title="List of spherical symmetry groups">Symmetry</a>: <a href="/wiki/Tetrahedral_symmetry" title="Tetrahedral symmetry">[3,3]</a>, (*332) </th> <th>[3,3]<sup>+</sup>, (332) </th></tr> <tr style="text-align:center;"> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_polyhedron-33-t0.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Uniform_polyhedron-33-t0.png/50px-Uniform_polyhedron-33-t0.png" decoding="async" width="50" height="54" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Uniform_polyhedron-33-t0.png/75px-Uniform_polyhedron-33-t0.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Uniform_polyhedron-33-t0.png/100px-Uniform_polyhedron-33-t0.png 2x" data-file-width="632" data-file-height="681" /></a></span> </td> <td><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/50px-Uniform_polyhedron-33-t01.png" decoding="async" width="50" height="53" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Uniform_polyhedron-33-t01.png/75px-Uniform_polyhedron-33-t01.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Uniform_polyhedron-33-t01.png/100px-Uniform_polyhedron-33-t01.png 2x" data-file-width="688" data-file-height="728" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_polyhedron-33-t1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Uniform_polyhedron-33-t1.svg/50px-Uniform_polyhedron-33-t1.svg.png" decoding="async" width="50" height="49" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Uniform_polyhedron-33-t1.svg/75px-Uniform_polyhedron-33-t1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Uniform_polyhedron-33-t1.svg/100px-Uniform_polyhedron-33-t1.svg.png 2x" data-file-width="658" data-file-height="646" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_polyhedron-33-t12.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Uniform_polyhedron-33-t12.png/50px-Uniform_polyhedron-33-t12.png" decoding="async" width="50" height="47" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Uniform_polyhedron-33-t12.png/75px-Uniform_polyhedron-33-t12.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Uniform_polyhedron-33-t12.png/100px-Uniform_polyhedron-33-t12.png 2x" data-file-width="736" data-file-height="687" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_polyhedron-33-t2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Uniform_polyhedron-33-t2.png/50px-Uniform_polyhedron-33-t2.png" decoding="async" width="50" height="45" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Uniform_polyhedron-33-t2.png/75px-Uniform_polyhedron-33-t2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/07/Uniform_polyhedron-33-t2.png/100px-Uniform_polyhedron-33-t2.png 2x" data-file-width="661" data-file-height="594" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_polyhedron-33-t02.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Uniform_polyhedron-33-t02.png/50px-Uniform_polyhedron-33-t02.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Uniform_polyhedron-33-t02.png/75px-Uniform_polyhedron-33-t02.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Uniform_polyhedron-33-t02.png/100px-Uniform_polyhedron-33-t02.png 2x" data-file-width="760" data-file-height="759" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_polyhedron-33-t012.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/Uniform_polyhedron-33-t012.png/50px-Uniform_polyhedron-33-t012.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/Uniform_polyhedron-33-t012.png/75px-Uniform_polyhedron-33-t012.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/Uniform_polyhedron-33-t012.png/100px-Uniform_polyhedron-33-t012.png 2x" data-file-width="762" data-file-height="756" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_polyhedron-33-s012.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Uniform_polyhedron-33-s012.svg/50px-Uniform_polyhedron-33-s012.svg.png" decoding="async" width="50" height="45" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Uniform_polyhedron-33-s012.svg/75px-Uniform_polyhedron-33-s012.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Uniform_polyhedron-33-s012.svg/100px-Uniform_polyhedron-33-s012.svg.png 2x" data-file-width="750" data-file-height="675" /></a></span> </td></tr> <tr style="text-align:center;"> <th><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> </th> <th><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/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> </th> <th><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> </th> <th><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/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> </th> <th><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/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> </th> <th><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/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> </th> <th><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/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/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> </th> <th><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/2/28/CDel_node_h.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/2/28/CDel_node_h.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/2/28/CDel_node_h.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span></span> </th></tr> <tr style="text-align:center;"> <td><a href="/wiki/Tetrahedron" title="Tetrahedron">{3,3}</a> </td> <td><a href="/wiki/Truncated_tetrahedron" title="Truncated tetrahedron">t{3,3}</a> </td> <td><a href="/wiki/Octahedron" title="Octahedron">r{3,3}</a> </td> <td><a href="/wiki/Truncated_tetrahedron" title="Truncated tetrahedron">t{3,3}</a> </td> <td><a href="/wiki/Tetrahedron" title="Tetrahedron">{3,3}</a> </td> <td><a href="/wiki/Cuboctahedron" title="Cuboctahedron">rr{3,3}</a> </td> <td><a href="/wiki/Truncated_octahedron" title="Truncated octahedron">tr{3,3}</a> </td> <td><a href="/wiki/Pseudoicosahedron" class="mw-redirect" title="Pseudoicosahedron">sr{3,3}</a> </td></tr> <tr> <th colspan="8">Duals to uniform polyhedra </th></tr> <tr style="text-align:center;"> <td><span typeof="mw:File"><a href="/wiki/File:Tetrahedron.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Tetrahedron.svg/50px-Tetrahedron.svg.png" decoding="async" width="50" height="47" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Tetrahedron.svg/75px-Tetrahedron.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Tetrahedron.svg/100px-Tetrahedron.svg.png 2x" data-file-width="570" data-file-height="540" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Triakistetrahedron.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Triakistetrahedron.jpg/50px-Triakistetrahedron.jpg" decoding="async" width="50" height="56" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Triakistetrahedron.jpg/75px-Triakistetrahedron.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/Triakistetrahedron.jpg/100px-Triakistetrahedron.jpg 2x" data-file-width="681" data-file-height="766" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Hexahedron.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Hexahedron.svg/50px-Hexahedron.svg.png" decoding="async" width="50" height="56" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Hexahedron.svg/75px-Hexahedron.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Hexahedron.svg/100px-Hexahedron.svg.png 2x" data-file-width="540" data-file-height="600" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Triakistetrahedron.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Triakistetrahedron.jpg/50px-Triakistetrahedron.jpg" decoding="async" width="50" height="56" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Triakistetrahedron.jpg/75px-Triakistetrahedron.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/Triakistetrahedron.jpg/100px-Triakistetrahedron.jpg 2x" data-file-width="681" data-file-height="766" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Tetrahedron.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Tetrahedron.svg/50px-Tetrahedron.svg.png" decoding="async" width="50" height="47" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Tetrahedron.svg/75px-Tetrahedron.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Tetrahedron.svg/100px-Tetrahedron.svg.png 2x" data-file-width="570" data-file-height="540" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Rhombicdodecahedron.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Rhombicdodecahedron.jpg/50px-Rhombicdodecahedron.jpg" decoding="async" width="50" height="44" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Rhombicdodecahedron.jpg/75px-Rhombicdodecahedron.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Rhombicdodecahedron.jpg/100px-Rhombicdodecahedron.jpg 2x" data-file-width="849" data-file-height="754" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Tetrakishexahedron.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/Tetrakishexahedron.jpg/50px-Tetrakishexahedron.jpg" decoding="async" width="50" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/Tetrakishexahedron.jpg/75px-Tetrakishexahedron.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/61/Tetrakishexahedron.jpg/100px-Tetrakishexahedron.jpg 2x" data-file-width="767" data-file-height="737" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dodecahedron.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Dodecahedron.svg/50px-Dodecahedron.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Dodecahedron.svg/75px-Dodecahedron.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Dodecahedron.svg/100px-Dodecahedron.svg.png 2x" data-file-width="300" data-file-height="300" /></a></span> </td></tr> <tr style="text-align:center;"> <td><a href="/wiki/Tetrahedron" title="Tetrahedron">V3.3.3</a> </td> <td><a class="mw-selflink selflink">V3.6.6</a> </td> <td><a href="/wiki/Cube" title="Cube">V3.3.3.3</a> </td> <td><a class="mw-selflink selflink">V3.6.6</a> </td> <td><a href="/wiki/Tetrahedron" title="Tetrahedron">V3.3.3</a> </td> <td><a href="/wiki/Rhombic_dodecahedron" title="Rhombic dodecahedron">V3.4.3.4</a> </td> <td><a href="/wiki/Tetrakis_hexahedron" title="Tetrakis hexahedron">V4.6.6</a> </td> <td><a href="/wiki/Pyritohedron" class="mw-redirect" title="Pyritohedron">V3.3.3.3.3</a> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Triakis_tetrahedron&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Truncated_triakis_tetrahedron" title="Truncated triakis tetrahedron">Truncated triakis tetrahedron</a></li></ul> <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=Triakis_tetrahedron&action=edit&section=8" title="Edit section: References"><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 class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">Conway, Symmetries of things, p.284</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://rechneronline.de/pi/triakis-tetrahedron.php">"Triakis Tetrahedron - Geometry Calculator"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Triakis+Tetrahedron+-+Geometry+Calculator&rft_id=https%3A%2F%2Frechneronline.de%2Fpi%2Ftriakis-tetrahedron.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATriakis+tetrahedron" class="Z3988"></span></span> </li> </ol></div></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilliams1979" class="citation book cs1"><a href="/wiki/Robert_Williams_(geometer)" title="Robert Williams (geometer)">Williams, Robert</a> (1979). <i>The Geometrical Foundation of Natural Structure: A Source Book of Design</i>. Dover Publications, Inc. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-486-23729-X" title="Special:BookSources/0-486-23729-X"><bdi>0-486-23729-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Geometrical+Foundation+of+Natural+Structure%3A+A+Source+Book+of+Design&rft.pub=Dover+Publications%2C+Inc&rft.date=1979&rft.isbn=0-486-23729-X&rft.aulast=Williams&rft.aufirst=Robert&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATriakis+tetrahedron" class="Z3988"></span> (Section 3-9)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWenninger1983" class="citation cs2"><a href="/wiki/Magnus_Wenninger" title="Magnus Wenninger">Wenninger, Magnus</a> (1983), <i>Dual Models</i>, <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FCBO9780511569371">10.1017/CBO9780511569371</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-54325-5" title="Special:BookSources/978-0-521-54325-5"><bdi>978-0-521-54325-5</bdi></a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0730208">0730208</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Dual+Models&rft.pub=Cambridge+University+Press&rft.date=1983&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D730208%23id-name%3DMR&rft_id=info%3Adoi%2F10.1017%2FCBO9780511569371&rft.isbn=978-0-521-54325-5&rft.aulast=Wenninger&rft.aufirst=Magnus&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATriakis+tetrahedron" class="Z3988"></span> (The thirteen semiregular convex polyhedra and their duals, Page 14, Triakistetrahedron)</li> <li><i>The Symmetries of Things</i> 2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-56881-220-5" title="Special:BookSources/978-1-56881-220-5">978-1-56881-220-5</a> <a rel="nofollow" class="external autonumber" href="https://web.archive.org/web/20100919143320/https://akpeters.com/product.asp?ProdCode=2205">[1]</a> (Chapter 21, Naming the Archimedean and Catalan polyhedra and tilings, page 284, Triakis tetrahedron )</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=Triakis_tetrahedron&action=edit&section=9" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite id="Reference-Mathworld-Triakis_tetrahedron"><a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W.</a>, "<a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/TriakisTetrahedron.html">Triakis tetrahedron</a>" ("<a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/CatalanSolid.html">Catalan solid</a>") at <i><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></i>.</cite></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Catalan_solids" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Catalan_solids" title="Template:Catalan solids"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Catalan_solids" title="Template talk:Catalan solids"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Catalan_solids" title="Special:EditPage/Template:Catalan solids"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Catalan_solids" style="font-size:114%;margin:0 4em"><a href="/wiki/Catalan_solid" title="Catalan solid">Catalan solids</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0;padding:0"><div style="padding:0 0.25em"> <table style="width:100%"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_4a.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Polyhedron_4a.png/90px-Polyhedron_4a.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Polyhedron_4a.png/135px-Polyhedron_4a.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Polyhedron_4a.png/180px-Polyhedron_4a.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a href="/wiki/Regular_tetrahedron" class="mw-redirect" title="Regular tetrahedron">Tetrahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Seed)</a> </td> <td rowspan="5"> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_8.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Polyhedron_8.png/90px-Polyhedron_8.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Polyhedron_8.png/135px-Polyhedron_8.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Polyhedron_8.png/180px-Polyhedron_8.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a href="/wiki/Regular_octahedron" class="mw-redirect" title="Regular octahedron">Octahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Dual)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_6_unchamfered.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Polyhedron_6_unchamfered.svg/90px-Polyhedron_6_unchamfered.svg.png" decoding="async" width="90" height="89" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Polyhedron_6_unchamfered.svg/135px-Polyhedron_6_unchamfered.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Polyhedron_6_unchamfered.svg/180px-Polyhedron_6_unchamfered.svg.png 2x" data-file-width="4520" data-file-height="4483" /></a></span><br /><a href="/wiki/Cube" title="Cube">Cube</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Seed)</a> </td> <td rowspan="5"> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_20.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Polyhedron_20.png/90px-Polyhedron_20.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Polyhedron_20.png/135px-Polyhedron_20.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Polyhedron_20.png/180px-Polyhedron_20.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a href="/wiki/Regular_icosahedron" title="Regular icosahedron">Icosahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Dual)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_12.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Polyhedron_12.png/90px-Polyhedron_12.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Polyhedron_12.png/135px-Polyhedron_12.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Polyhedron_12.png/180px-Polyhedron_12.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a href="/wiki/Regular_dodecahedron" title="Regular dodecahedron">Dodecahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Seed)</a> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_4a_dual.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Polyhedron_truncated_4a_dual.png/90px-Polyhedron_truncated_4a_dual.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Polyhedron_truncated_4a_dual.png/135px-Polyhedron_truncated_4a_dual.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/54/Polyhedron_truncated_4a_dual.png/180px-Polyhedron_truncated_4a_dual.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a class="mw-selflink selflink">Triakis tetrahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Needle)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_4b_dual.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Polyhedron_truncated_4b_dual.png/90px-Polyhedron_truncated_4b_dual.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Polyhedron_truncated_4b_dual.png/135px-Polyhedron_truncated_4b_dual.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Polyhedron_truncated_4b_dual.png/180px-Polyhedron_truncated_4b_dual.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a class="mw-selflink selflink">Triakis tetrahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Kis)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_6_dual.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Polyhedron_truncated_6_dual.png/90px-Polyhedron_truncated_6_dual.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Polyhedron_truncated_6_dual.png/135px-Polyhedron_truncated_6_dual.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Polyhedron_truncated_6_dual.png/180px-Polyhedron_truncated_6_dual.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a href="/wiki/Triakis_octahedron" title="Triakis octahedron">Triakis octahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Needle)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_8_dual.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Polyhedron_truncated_8_dual.png/90px-Polyhedron_truncated_8_dual.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Polyhedron_truncated_8_dual.png/135px-Polyhedron_truncated_8_dual.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Polyhedron_truncated_8_dual.png/180px-Polyhedron_truncated_8_dual.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a href="/wiki/Tetrakis_hexahedron" title="Tetrakis hexahedron">Tetrakis hexahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Kis)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_12_dual.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Polyhedron_truncated_12_dual.png/90px-Polyhedron_truncated_12_dual.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Polyhedron_truncated_12_dual.png/135px-Polyhedron_truncated_12_dual.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Polyhedron_truncated_12_dual.png/180px-Polyhedron_truncated_12_dual.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a href="/wiki/Triakis_icosahedron" title="Triakis icosahedron">Triakis icosahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Needle)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_20_dual.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Polyhedron_truncated_20_dual.png/90px-Polyhedron_truncated_20_dual.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Polyhedron_truncated_20_dual.png/135px-Polyhedron_truncated_20_dual.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/24/Polyhedron_truncated_20_dual.png/180px-Polyhedron_truncated_20_dual.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a href="/wiki/Pentakis_dodecahedron" title="Pentakis dodecahedron">Pentakis dodecahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Kis)</a> </td></tr> <tr> <td colspan="2"><span typeof="mw:File"><a href="/wiki/File:Polyhedron_4-4_dual.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/74/Polyhedron_4-4_dual.png/180px-Polyhedron_4-4_dual.png" decoding="async" width="180" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/74/Polyhedron_4-4_dual.png/270px-Polyhedron_4-4_dual.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/74/Polyhedron_4-4_dual.png/360px-Polyhedron_4-4_dual.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><big><a href="/wiki/Cube" title="Cube">Rhombic hexahedron</a></big><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Join)</a> </td> <td colspan="2"><span typeof="mw:File"><a href="/wiki/File:Polyhedron_6-8_dual.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Polyhedron_6-8_dual.png/180px-Polyhedron_6-8_dual.png" decoding="async" width="180" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Polyhedron_6-8_dual.png/270px-Polyhedron_6-8_dual.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/05/Polyhedron_6-8_dual.png/360px-Polyhedron_6-8_dual.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><big><a href="/wiki/Rhombic_dodecahedron" title="Rhombic dodecahedron">Rhombic dodecahedron</a></big><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Join)</a> </td> <td colspan="2"><span typeof="mw:File"><a href="/wiki/File:Polyhedron_12-20_dual.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Polyhedron_12-20_dual.png/180px-Polyhedron_12-20_dual.png" decoding="async" width="180" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Polyhedron_12-20_dual.png/270px-Polyhedron_12-20_dual.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Polyhedron_12-20_dual.png/360px-Polyhedron_12-20_dual.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><big><a href="/wiki/Rhombic_triacontahedron" title="Rhombic triacontahedron">Rhombic triacontahedron</a></big><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Join)</a> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_small_rhombi_4-4_dual_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Polyhedron_small_rhombi_4-4_dual_max.png/90px-Polyhedron_small_rhombi_4-4_dual_max.png" decoding="async" width="90" height="91" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Polyhedron_small_rhombi_4-4_dual_max.png/135px-Polyhedron_small_rhombi_4-4_dual_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Polyhedron_small_rhombi_4-4_dual_max.png/180px-Polyhedron_small_rhombi_4-4_dual_max.png 2x" data-file-width="3872" data-file-height="3927" /></a></span><br /><a href="/wiki/Rhombic_dodecahedron" title="Rhombic dodecahedron">Deltoidal dodecahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Ortho)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_great_rhombi_4-4_dual_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Polyhedron_great_rhombi_4-4_dual_max.png/90px-Polyhedron_great_rhombi_4-4_dual_max.png" decoding="async" width="90" height="91" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Polyhedron_great_rhombi_4-4_dual_max.png/135px-Polyhedron_great_rhombi_4-4_dual_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Polyhedron_great_rhombi_4-4_dual_max.png/180px-Polyhedron_great_rhombi_4-4_dual_max.png 2x" data-file-width="3861" data-file-height="3916" /></a></span><br /><a href="/wiki/Tetrakis_hexahedron" title="Tetrakis hexahedron">Disdyakis hexahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Meta)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_small_rhombi_6-8_dual_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Polyhedron_small_rhombi_6-8_dual_max.png/90px-Polyhedron_small_rhombi_6-8_dual_max.png" decoding="async" width="90" height="92" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Polyhedron_small_rhombi_6-8_dual_max.png/135px-Polyhedron_small_rhombi_6-8_dual_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Polyhedron_small_rhombi_6-8_dual_max.png/180px-Polyhedron_small_rhombi_6-8_dual_max.png 2x" data-file-width="3850" data-file-height="3923" /></a></span><br /><a href="/wiki/Deltoidal_icositetrahedron" title="Deltoidal icositetrahedron">Deltoidal icositetrahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Ortho)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_great_rhombi_6-8_dual_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Polyhedron_great_rhombi_6-8_dual_max.png/90px-Polyhedron_great_rhombi_6-8_dual_max.png" decoding="async" width="90" height="91" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Polyhedron_great_rhombi_6-8_dual_max.png/135px-Polyhedron_great_rhombi_6-8_dual_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Polyhedron_great_rhombi_6-8_dual_max.png/180px-Polyhedron_great_rhombi_6-8_dual_max.png 2x" data-file-width="3878" data-file-height="3928" /></a></span><br /><a href="/wiki/Disdyakis_dodecahedron" title="Disdyakis dodecahedron">Disdyakis dodecahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Meta)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_small_rhombi_12-20_dual_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Polyhedron_small_rhombi_12-20_dual_max.png/90px-Polyhedron_small_rhombi_12-20_dual_max.png" decoding="async" width="90" height="89" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Polyhedron_small_rhombi_12-20_dual_max.png/135px-Polyhedron_small_rhombi_12-20_dual_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/28/Polyhedron_small_rhombi_12-20_dual_max.png/180px-Polyhedron_small_rhombi_12-20_dual_max.png 2x" data-file-width="3954" data-file-height="3911" /></a></span><br /><a href="/wiki/Deltoidal_hexecontahedron" title="Deltoidal hexecontahedron">Deltoidal hexecontahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Ortho)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_great_rhombi_12-20_dual_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Polyhedron_great_rhombi_12-20_dual_max.png/90px-Polyhedron_great_rhombi_12-20_dual_max.png" decoding="async" width="90" height="86" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Polyhedron_great_rhombi_12-20_dual_max.png/135px-Polyhedron_great_rhombi_12-20_dual_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Polyhedron_great_rhombi_12-20_dual_max.png/180px-Polyhedron_great_rhombi_12-20_dual_max.png 2x" data-file-width="3928" data-file-height="3773" /></a></span><br /><a href="/wiki/Disdyakis_triacontahedron" title="Disdyakis triacontahedron">Disdyakis triacontahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Meta)</a> </td></tr> <tr> <td colspan="2"><span typeof="mw:File"><a href="/wiki/File:Polyhedron_snub_4-4_right_dual_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Polyhedron_snub_4-4_right_dual_max.png/82px-Polyhedron_snub_4-4_right_dual_max.png" decoding="async" width="82" height="77" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Polyhedron_snub_4-4_right_dual_max.png/123px-Polyhedron_snub_4-4_right_dual_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Polyhedron_snub_4-4_right_dual_max.png/164px-Polyhedron_snub_4-4_right_dual_max.png 2x" data-file-width="3982" data-file-height="3757" /></a></span><span typeof="mw:File"><a href="/wiki/File:Polyhedron_snub_4-4_left_dual_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Polyhedron_snub_4-4_left_dual_max.png/80px-Polyhedron_snub_4-4_left_dual_max.png" decoding="async" width="80" height="87" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Polyhedron_snub_4-4_left_dual_max.png/120px-Polyhedron_snub_4-4_left_dual_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/Polyhedron_snub_4-4_left_dual_max.png/160px-Polyhedron_snub_4-4_left_dual_max.png 2x" data-file-width="3652" data-file-height="3960" /></a></span><br /><a href="/wiki/Regular_dodecahedron" title="Regular dodecahedron">Pentagonal dodecahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Gyro)</a> </td> <td colspan="2"><span typeof="mw:File"><a href="/wiki/File:Polyhedron_snub_6-8_right_dual_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Polyhedron_snub_6-8_right_dual_max.png/80px-Polyhedron_snub_6-8_right_dual_max.png" decoding="async" width="80" height="81" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Polyhedron_snub_6-8_right_dual_max.png/120px-Polyhedron_snub_6-8_right_dual_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Polyhedron_snub_6-8_right_dual_max.png/160px-Polyhedron_snub_6-8_right_dual_max.png 2x" data-file-width="3833" data-file-height="3889" /></a></span><span typeof="mw:File"><a href="/wiki/File:Polyhedron_snub_6-8_left_dual_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Polyhedron_snub_6-8_left_dual_max.png/80px-Polyhedron_snub_6-8_left_dual_max.png" decoding="async" width="80" height="81" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Polyhedron_snub_6-8_left_dual_max.png/120px-Polyhedron_snub_6-8_left_dual_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Polyhedron_snub_6-8_left_dual_max.png/160px-Polyhedron_snub_6-8_left_dual_max.png 2x" data-file-width="3833" data-file-height="3895" /></a></span><br /><a href="/wiki/Pentagonal_icositetrahedron" title="Pentagonal icositetrahedron">Pentagonal icositetrahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Gyro)</a> </td> <td colspan="2"><span typeof="mw:File"><a href="/wiki/File:Polyhedron_snub_12-20_right_dual_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a8/Polyhedron_snub_12-20_right_dual_max.png/80px-Polyhedron_snub_12-20_right_dual_max.png" decoding="async" width="80" height="79" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a8/Polyhedron_snub_12-20_right_dual_max.png/120px-Polyhedron_snub_12-20_right_dual_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a8/Polyhedron_snub_12-20_right_dual_max.png/160px-Polyhedron_snub_12-20_right_dual_max.png 2x" data-file-width="3928" data-file-height="3893" /></a></span><span typeof="mw:File"><a href="/wiki/File:Polyhedron_snub_12-20_left_dual_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Polyhedron_snub_12-20_left_dual_max.png/80px-Polyhedron_snub_12-20_left_dual_max.png" decoding="async" width="80" height="79" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Polyhedron_snub_12-20_left_dual_max.png/120px-Polyhedron_snub_12-20_left_dual_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/30/Polyhedron_snub_12-20_left_dual_max.png/160px-Polyhedron_snub_12-20_left_dual_max.png 2x" data-file-width="3939" data-file-height="3877" /></a></span><br /><a href="/wiki/Pentagonal_hexecontahedron" title="Pentagonal hexecontahedron">Pentagonal hexecontahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Gyro)</a> </td></tr> <tr> <td colspan="8"> <div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Archimedean_duals" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Archimedean_duals" style="font-size:114%;margin:0 4em"><a href="/wiki/Archimedean_solid" title="Archimedean solid">Archimedean</a> duals</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0;padding:0"><div style="padding:0 0.25em"> <table style="width:100%"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_4a.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Polyhedron_4a.png/90px-Polyhedron_4a.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Polyhedron_4a.png/135px-Polyhedron_4a.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Polyhedron_4a.png/180px-Polyhedron_4a.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a href="/wiki/Regular_tetrahedron" class="mw-redirect" title="Regular tetrahedron">Tetrahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Seed)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_4b.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Polyhedron_4b.png/90px-Polyhedron_4b.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Polyhedron_4b.png/135px-Polyhedron_4b.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Polyhedron_4b.png/180px-Polyhedron_4b.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a href="/wiki/Regular_tetrahedron" class="mw-redirect" title="Regular tetrahedron">Tetrahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Dual)</a> </td> <td rowspan="5"> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_6_unchamfered.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Polyhedron_6_unchamfered.svg/90px-Polyhedron_6_unchamfered.svg.png" decoding="async" width="90" height="89" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Polyhedron_6_unchamfered.svg/135px-Polyhedron_6_unchamfered.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Polyhedron_6_unchamfered.svg/180px-Polyhedron_6_unchamfered.svg.png 2x" data-file-width="4520" data-file-height="4483" /></a></span><br /><a href="/wiki/Cube" title="Cube">Cube</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Seed)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_8.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Polyhedron_8.png/90px-Polyhedron_8.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Polyhedron_8.png/135px-Polyhedron_8.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Polyhedron_8.png/180px-Polyhedron_8.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a href="/wiki/Regular_octahedron" class="mw-redirect" title="Regular octahedron">Octahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Dual)</a> </td> <td rowspan="5"> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_12.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Polyhedron_12.png/90px-Polyhedron_12.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Polyhedron_12.png/135px-Polyhedron_12.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Polyhedron_12.png/180px-Polyhedron_12.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a href="/wiki/Regular_dodecahedron" title="Regular dodecahedron">Dodecahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Seed)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_20.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Polyhedron_20.png/90px-Polyhedron_20.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Polyhedron_20.png/135px-Polyhedron_20.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Polyhedron_20.png/180px-Polyhedron_20.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a href="/wiki/Regular_icosahedron" title="Regular icosahedron">Icosahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Dual)</a> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_4a.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Polyhedron_truncated_4a.png/90px-Polyhedron_truncated_4a.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Polyhedron_truncated_4a.png/135px-Polyhedron_truncated_4a.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Polyhedron_truncated_4a.png/180px-Polyhedron_truncated_4a.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a href="/wiki/Truncated_tetrahedron" title="Truncated tetrahedron">Truncated tetrahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Truncate)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_4b.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Polyhedron_truncated_4b.png/90px-Polyhedron_truncated_4b.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Polyhedron_truncated_4b.png/135px-Polyhedron_truncated_4b.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Polyhedron_truncated_4b.png/180px-Polyhedron_truncated_4b.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a href="/wiki/Truncated_tetrahedron" title="Truncated tetrahedron">Truncated tetrahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Zip)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_6.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Polyhedron_truncated_6.png/90px-Polyhedron_truncated_6.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Polyhedron_truncated_6.png/135px-Polyhedron_truncated_6.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Polyhedron_truncated_6.png/180px-Polyhedron_truncated_6.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a href="/wiki/Truncated_cube" title="Truncated cube">Truncated cube</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Truncate)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_8.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Polyhedron_truncated_8.png/90px-Polyhedron_truncated_8.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Polyhedron_truncated_8.png/135px-Polyhedron_truncated_8.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Polyhedron_truncated_8.png/180px-Polyhedron_truncated_8.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a href="/wiki/Truncated_octahedron" title="Truncated octahedron">Truncated octahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Zip)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_12.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Polyhedron_truncated_12.png/90px-Polyhedron_truncated_12.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Polyhedron_truncated_12.png/135px-Polyhedron_truncated_12.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Polyhedron_truncated_12.png/180px-Polyhedron_truncated_12.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a href="/wiki/Truncated_dodecahedron" title="Truncated dodecahedron">Truncated dodecahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Truncate)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_20.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Polyhedron_truncated_20.png/90px-Polyhedron_truncated_20.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Polyhedron_truncated_20.png/135px-Polyhedron_truncated_20.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Polyhedron_truncated_20.png/180px-Polyhedron_truncated_20.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><a href="/wiki/Truncated_icosahedron" title="Truncated icosahedron">Truncated icosahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Zip)</a> </td></tr> <tr> <td colspan="2"><span typeof="mw:File"><a href="/wiki/File:Polyhedron_4-4.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Polyhedron_4-4.png/180px-Polyhedron_4-4.png" decoding="async" width="180" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Polyhedron_4-4.png/270px-Polyhedron_4-4.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/66/Polyhedron_4-4.png/360px-Polyhedron_4-4.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><big><a href="/wiki/Octahedron" title="Octahedron">Tetratetrahedron</a></big><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Ambo)</a> </td> <td colspan="2"><span typeof="mw:File"><a href="/wiki/File:Polyhedron_6-8.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Polyhedron_6-8.png/180px-Polyhedron_6-8.png" decoding="async" width="180" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Polyhedron_6-8.png/270px-Polyhedron_6-8.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Polyhedron_6-8.png/360px-Polyhedron_6-8.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><big><a href="/wiki/Cuboctahedron" title="Cuboctahedron">Cuboctahedron</a></big><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Ambo)</a> </td> <td colspan="2"><span typeof="mw:File"><a href="/wiki/File:Polyhedron_12-20.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Polyhedron_12-20.png/180px-Polyhedron_12-20.png" decoding="async" width="180" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Polyhedron_12-20.png/270px-Polyhedron_12-20.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Polyhedron_12-20.png/360px-Polyhedron_12-20.png 2x" data-file-width="4000" data-file-height="4000" /></a></span><br /><big><a href="/wiki/Icosidodecahedron" title="Icosidodecahedron">Icosidodecahedron</a></big><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Ambo)</a> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_small_rhombi_4-4_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Polyhedron_small_rhombi_4-4_max.png/90px-Polyhedron_small_rhombi_4-4_max.png" decoding="async" width="90" height="86" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Polyhedron_small_rhombi_4-4_max.png/135px-Polyhedron_small_rhombi_4-4_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/28/Polyhedron_small_rhombi_4-4_max.png/180px-Polyhedron_small_rhombi_4-4_max.png 2x" data-file-width="3850" data-file-height="3680" /></a></span><br /><a href="/wiki/Cuboctahedron" title="Cuboctahedron">Rhombitetratetrahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Expand)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_great_rhombi_4-4_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Polyhedron_great_rhombi_4-4_max.png/90px-Polyhedron_great_rhombi_4-4_max.png" decoding="async" width="90" height="88" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Polyhedron_great_rhombi_4-4_max.png/135px-Polyhedron_great_rhombi_4-4_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Polyhedron_great_rhombi_4-4_max.png/180px-Polyhedron_great_rhombi_4-4_max.png 2x" data-file-width="3922" data-file-height="3854" /></a></span><br /><a href="/wiki/Truncated_octahedron" title="Truncated octahedron">Truncated tetratetrahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Bevel)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_small_rhombi_6-8_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Polyhedron_small_rhombi_6-8_max.png/90px-Polyhedron_small_rhombi_6-8_max.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Polyhedron_small_rhombi_6-8_max.png/135px-Polyhedron_small_rhombi_6-8_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/46/Polyhedron_small_rhombi_6-8_max.png/180px-Polyhedron_small_rhombi_6-8_max.png 2x" data-file-width="3906" data-file-height="3910" /></a></span><br /><a href="/wiki/Rhombicuboctahedron" title="Rhombicuboctahedron">Rhombicuboctahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Expand)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_great_rhombi_6-8_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Polyhedron_great_rhombi_6-8_max.png/90px-Polyhedron_great_rhombi_6-8_max.png" decoding="async" width="90" height="88" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Polyhedron_great_rhombi_6-8_max.png/135px-Polyhedron_great_rhombi_6-8_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Polyhedron_great_rhombi_6-8_max.png/180px-Polyhedron_great_rhombi_6-8_max.png 2x" data-file-width="3860" data-file-height="3795" /></a></span><br /><a href="/wiki/Truncated_cuboctahedron" title="Truncated cuboctahedron">Truncated cuboctahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Bevel)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_small_rhombi_12-20_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Polyhedron_small_rhombi_12-20_max.png/90px-Polyhedron_small_rhombi_12-20_max.png" decoding="async" width="90" height="91" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Polyhedron_small_rhombi_12-20_max.png/135px-Polyhedron_small_rhombi_12-20_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Polyhedron_small_rhombi_12-20_max.png/180px-Polyhedron_small_rhombi_12-20_max.png 2x" data-file-width="3973" data-file-height="4000" /></a></span><br /><a href="/wiki/Rhombicosidodecahedron" title="Rhombicosidodecahedron">Rhombicosidodecahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Expand)</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_great_rhombi_12-20_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Polyhedron_great_rhombi_12-20_max.png/90px-Polyhedron_great_rhombi_12-20_max.png" decoding="async" width="90" height="91" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Polyhedron_great_rhombi_12-20_max.png/135px-Polyhedron_great_rhombi_12-20_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Polyhedron_great_rhombi_12-20_max.png/180px-Polyhedron_great_rhombi_12-20_max.png 2x" data-file-width="3943" data-file-height="3977" /></a></span><br /><a href="/wiki/Truncated_icosidodecahedron" title="Truncated icosidodecahedron">Truncated icosidodecahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Bevel)</a> </td></tr> <tr> <td colspan="2"><span typeof="mw:File"><a href="/wiki/File:Polyhedron_snub_4-4_left_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Polyhedron_snub_4-4_left_max.png/88px-Polyhedron_snub_4-4_left_max.png" decoding="async" width="88" height="79" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Polyhedron_snub_4-4_left_max.png/132px-Polyhedron_snub_4-4_left_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Polyhedron_snub_4-4_left_max.png/176px-Polyhedron_snub_4-4_left_max.png 2x" data-file-width="3926" data-file-height="3526" /></a></span><span typeof="mw:File"><a href="/wiki/File:Polyhedron_snub_4-4_right_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Polyhedron_snub_4-4_right_max.png/80px-Polyhedron_snub_4-4_right_max.png" decoding="async" width="80" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Polyhedron_snub_4-4_right_max.png/120px-Polyhedron_snub_4-4_right_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Polyhedron_snub_4-4_right_max.png/160px-Polyhedron_snub_4-4_right_max.png 2x" data-file-width="3408" data-file-height="3829" /></a></span><br /><a href="/wiki/Regular_icosahedron" title="Regular icosahedron">Snub tetrahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Snub)</a> </td> <td colspan="2"><span typeof="mw:File"><a href="/wiki/File:Polyhedron_snub_6-8_left_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Polyhedron_snub_6-8_left_max.png/80px-Polyhedron_snub_6-8_left_max.png" decoding="async" width="80" height="77" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Polyhedron_snub_6-8_left_max.png/120px-Polyhedron_snub_6-8_left_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Polyhedron_snub_6-8_left_max.png/160px-Polyhedron_snub_6-8_left_max.png 2x" data-file-width="3932" data-file-height="3804" /></a></span><span typeof="mw:File"><a href="/wiki/File:Polyhedron_snub_6-8_right_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Polyhedron_snub_6-8_right_max.png/80px-Polyhedron_snub_6-8_right_max.png" decoding="async" width="80" height="79" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Polyhedron_snub_6-8_right_max.png/120px-Polyhedron_snub_6-8_right_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Polyhedron_snub_6-8_right_max.png/160px-Polyhedron_snub_6-8_right_max.png 2x" data-file-width="3905" data-file-height="3860" /></a></span><br /><a href="/wiki/Snub_cube" title="Snub cube">Snub cube</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Snub)</a> </td> <td colspan="2"><span typeof="mw:File"><a href="/wiki/File:Polyhedron_snub_12-20_left_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Polyhedron_snub_12-20_left_max.png/80px-Polyhedron_snub_12-20_left_max.png" decoding="async" width="80" height="81" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Polyhedron_snub_12-20_left_max.png/120px-Polyhedron_snub_12-20_left_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/Polyhedron_snub_12-20_left_max.png/160px-Polyhedron_snub_12-20_left_max.png 2x" data-file-width="3966" data-file-height="4000" /></a></span><span typeof="mw:File"><a href="/wiki/File:Polyhedron_snub_12-20_right_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Polyhedron_snub_12-20_right_max.png/80px-Polyhedron_snub_12-20_right_max.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Polyhedron_snub_12-20_right_max.png/120px-Polyhedron_snub_12-20_right_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Polyhedron_snub_12-20_right_max.png/160px-Polyhedron_snub_12-20_right_max.png 2x" data-file-width="3983" data-file-height="4000" /></a></span><br /><a href="/wiki/Snub_dodecahedron" title="Snub dodecahedron">Snub dodecahedron</a><br /><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">(Snub)</a> </td></tr></tbody></table> </div></td></tr></tbody></table></div> </td></tr></tbody></table> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><style data-mw-deduplicate="TemplateStyles:r886047488">.mw-parser-output .nobold{font-weight:normal}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886047488"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886047488"></div><div role="navigation" class="navbox" aria-labelledby="Convex_polyhedra" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Convex_polyhedron_navigator" title="Template:Convex polyhedron navigator"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Convex_polyhedron_navigator" title="Template talk:Convex polyhedron navigator"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Convex_polyhedron_navigator" title="Special:EditPage/Template:Convex polyhedron navigator"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Convex_polyhedra" style="font-size:114%;margin:0 4em">Convex <a href="/wiki/Polyhedron" title="Polyhedron">polyhedra</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Platonic_solid" title="Platonic solid">Platonic solids</a> <span class="nobold">(<a href="/wiki/Regular_polyhedron" title="Regular polyhedron">regular</a>)</span></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Tetrahedron#Regular_tetrahedron" title="Tetrahedron">tetrahedron</a></li> <li><a href="/wiki/Cube" title="Cube">cube</a></li> <li><a href="/wiki/Octahedron" title="Octahedron">octahedron</a></li> <li><a href="/wiki/Regular_dodecahedron" title="Regular dodecahedron">dodecahedron</a></li> <li><a href="/wiki/Regular_icosahedron" title="Regular icosahedron">icosahedron</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Archimedean_solid" title="Archimedean solid">Archimedean solids</a><br /><span class="nobold">(<a href="/wiki/Semiregular_polyhedron" title="Semiregular polyhedron">semiregular</a> or <a href="/wiki/Uniform_polyhedron" title="Uniform polyhedron">uniform</a>)</span></div></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Truncated_tetrahedron" title="Truncated tetrahedron">truncated tetrahedron</a></li> <li><a href="/wiki/Cuboctahedron" title="Cuboctahedron">cuboctahedron</a></li> <li><a href="/wiki/Truncated_cube" title="Truncated cube">truncated cube</a></li> <li><a href="/wiki/Truncated_octahedron" title="Truncated octahedron">truncated octahedron</a></li> <li><a href="/wiki/Rhombicuboctahedron" title="Rhombicuboctahedron">rhombicuboctahedron</a></li> <li><a href="/wiki/Truncated_cuboctahedron" title="Truncated cuboctahedron">truncated cuboctahedron</a></li> <li><a href="/wiki/Snub_cube" title="Snub cube">snub cube</a></li> <li><a href="/wiki/Icosidodecahedron" title="Icosidodecahedron">icosidodecahedron</a></li> <li><a href="/wiki/Truncated_dodecahedron" title="Truncated dodecahedron">truncated dodecahedron</a></li> <li><a href="/wiki/Truncated_icosahedron" title="Truncated icosahedron">truncated icosahedron</a></li> <li><a href="/wiki/Rhombicosidodecahedron" title="Rhombicosidodecahedron">rhombicosidodecahedron</a></li> <li><a href="/wiki/Truncated_icosidodecahedron" title="Truncated icosidodecahedron">truncated icosidodecahedron</a></li> <li><a href="/wiki/Snub_dodecahedron" title="Snub dodecahedron">snub dodecahedron</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Catalan_solid" title="Catalan solid">Catalan solids</a><br /><span class="nobold">(duals of Archimedean)</span></div></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">triakis tetrahedron</a></li> <li><a href="/wiki/Rhombic_dodecahedron" title="Rhombic dodecahedron">rhombic dodecahedron</a></li> <li><a href="/wiki/Triakis_octahedron" title="Triakis octahedron">triakis octahedron</a></li> <li><a href="/wiki/Tetrakis_hexahedron" title="Tetrakis hexahedron">tetrakis hexahedron</a></li> <li><a href="/wiki/Deltoidal_icositetrahedron" title="Deltoidal icositetrahedron">deltoidal icositetrahedron</a></li> <li><a href="/wiki/Disdyakis_dodecahedron" title="Disdyakis dodecahedron">disdyakis dodecahedron</a></li> <li><a href="/wiki/Pentagonal_icositetrahedron" title="Pentagonal icositetrahedron">pentagonal icositetrahedron</a></li> <li><a href="/wiki/Rhombic_triacontahedron" title="Rhombic triacontahedron">rhombic triacontahedron</a></li> <li><a href="/wiki/Triakis_icosahedron" title="Triakis icosahedron">triakis icosahedron</a></li> <li><a href="/wiki/Pentakis_dodecahedron" title="Pentakis dodecahedron">pentakis dodecahedron</a></li> <li><a href="/wiki/Deltoidal_hexecontahedron" title="Deltoidal hexecontahedron">deltoidal hexecontahedron</a></li> <li><a href="/wiki/Disdyakis_triacontahedron" title="Disdyakis triacontahedron">disdyakis triacontahedron</a></li> <li><a href="/wiki/Pentagonal_hexecontahedron" title="Pentagonal hexecontahedron">pentagonal hexecontahedron</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Dihedral regular</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Dihedron" title="Dihedron">dihedron</a></i></li> <li><i><a href="/wiki/Hosohedron" title="Hosohedron">hosohedron</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Dihedral uniform</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Prism_(geometry)" title="Prism (geometry)">prisms</a></li> <li><a href="/wiki/Antiprism" title="Antiprism">antiprisms</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">duals:</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bipyramid" title="Bipyramid">bipyramids</a></li> <li><a href="/wiki/Trapezohedron" title="Trapezohedron">trapezohedra</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Dihedral others</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Pyramid_(geometry)" title="Pyramid (geometry)">pyramids</a></li> <li><a href="/wiki/Truncated_trapezohedron" title="Truncated trapezohedron">truncated trapezohedra</a></li> <li><a href="/wiki/Gyroelongated_bipyramid" title="Gyroelongated bipyramid">gyroelongated bipyramid</a></li> <li><a href="/wiki/Cupola_(geometry)" title="Cupola (geometry)">cupola</a></li> <li><a href="/wiki/Bicupola_(geometry)" class="mw-redirect" title="Bicupola (geometry)">bicupola</a></li> <li><a href="/wiki/Frustum" title="Frustum">frustum</a></li> <li><a href="/wiki/Bifrustum" title="Bifrustum">bifrustum</a></li> <li><a href="/wiki/Rotunda_(geometry)" title="Rotunda (geometry)">rotunda</a></li> <li><a href="/wiki/Birotunda" title="Birotunda">birotunda</a></li> <li><a href="/wiki/Prismatoid" title="Prismatoid">prismatoid</a></li> <li><a href="/wiki/Scutoid" title="Scutoid">scutoid</a></li></ul> </div></td></tr><tr><td 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