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Available in 25 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-25" 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">25 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D0%B0%D0%BD%D0%B3%D1%83%D0%BB%D0%B8%D1%80%D0%B0%D0%BD_%D0%BF%D1%80%D0%B5%D1%81%D0%B5%D1%87%D0%B5%D0%BD_%D1%82%D0%B5%D1%82%D1%80%D0%B0%D0%B5%D0%B4%D1%8A%D1%80" title="Триангулиран пресечен тетраедър – Bulgarian" lang="bg" hreflang="bg" data-title="Триангулиран пресечен тетраедър" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Tetr%C3%A0edre_truncat" title="Tetràedre truncat – Catalan" lang="ca" hreflang="ca" data-title="Tetràedre truncat" 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/Tetraederstumpf" title="Tetraederstumpf – German" lang="de" hreflang="de" data-title="Tetraederstumpf" 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%9A%CF%8C%CE%BB%CE%BF%CF%85%CF%81%CE%BF_%CF%84%CE%B5%CF%84%CF%81%CE%AC%CE%B5%CE%B4%CF%81%CE%BF" title="Κόλουρο τετράεδρο – Greek" lang="el" hreflang="el" data-title="Κόλουρο 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/Tetraedro_truncado" title="Tetraedro truncado – Spanish" lang="es" hreflang="es" data-title="Tetraedro truncado" 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/Senpintigita_kvaredro" title="Senpintigita kvaredro – Esperanto" lang="eo" hreflang="eo" data-title="Senpintigita 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/Tetraedro_moztu" title="Tetraedro moztu – Basque" lang="eu" hreflang="eu" data-title="Tetraedro moztu" 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/%DA%86%D9%87%D8%A7%D8%B1%D9%88%D8%AC%D9%87%DB%8C_%D8%A8%D8%B1%DB%8C%D8%AF%D9%87%E2%80%8C%D8%B4%D8%AF%D9%87" title="چهاروجهی بریده‌شده – Persian" lang="fa" hreflang="fa" data-title="چهاروجهی بریده‌شده" 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/T%C3%A9tra%C3%A8dre_tronqu%C3%A9" title="Tétraèdre tronqué – French" lang="fr" hreflang="fr" data-title="Tétraèdre tronqué" 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/%EA%B9%8E%EC%9D%80_%EC%A0%95%EC%82%AC%EB%A9%B4%EC%B2%B4" title="깎은 정사면체 – Korean" lang="ko" hreflang="ko" data-title="깎은 정사면체" 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/Tetraedro_troncato" title="Tetraedro troncato – Italian" lang="it" hreflang="it" data-title="Tetraedro troncato" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%A8%D7%91%D7%A2%D7%95%D7%9F_%D7%A7%D7%98%D7%95%D7%9D" title="ארבעון קטום – Hebrew" lang="he" hreflang="he" data-title="ארבעון קטום" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Afgeknotte_tetra%C3%ABder" title="Afgeknotte tetraëder – Dutch" lang="nl" hreflang="nl" data-title="Afgeknotte tetraëder" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%88%87%E9%A0%82%E5%9B%9B%E9%9D%A2%E4%BD%93" title="切頂四面体 – Japanese" lang="ja" hreflang="ja" data-title="切頂四面体" 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/Avstumpet_tetraeder" title="Avstumpet tetraeder – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Avstumpet tetraeder" 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-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Avkutta_tetraeder" title="Avkutta tetraeder – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Avkutta tetraeder" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Czworo%C5%9Bcian_%C5%9Bci%C4%99ty" title="Czworościan ścięty – Polish" lang="pl" hreflang="pl" data-title="Czworościan ścięty" 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_truncado" title="Tetraedro truncado – Portuguese" lang="pt" hreflang="pt" data-title="Tetraedro truncado" 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_trunchiat" title="Tetraedru trunchiat – Romanian" lang="ro" hreflang="ro" data-title="Tetraedru trunchiat" 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%A3%D1%81%D0%B5%D1%87%D1%91%D0%BD%D0%BD%D1%8B%D0%B9_%D1%82%D0%B5%D1%82%D1%80%D0%B0%D1%8D%D0%B4%D1%80" title="Усечённый тетраэдр – Russian" lang="ru" hreflang="ru" data-title="Усечённый тетраэдр" 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/Prisekani_tetraeder" title="Prisekani tetraeder – Slovenian" lang="sl" hreflang="sl" data-title="Prisekani tetraeder" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Stympad_tetraeder" title="Stympad tetraeder – Swedish" lang="sv" hreflang="sv" data-title="Stympad tetraeder" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%97%E0%B8%A3%E0%B8%87%E0%B8%AA%E0%B8%B5%E0%B9%88%E0%B8%AB%E0%B8%99%E0%B9%89%E0%B8%B2%E0%B8%9B%E0%B8%A5%E0%B8%B2%E0%B8%A2%E0%B8%95%E0%B8%B1%E0%B8%94" title="ทรงสี่หน้าปลายตัด – Thai" lang="th" hreflang="th" data-title="ทรงสี่หน้าปลายตัด" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%97%D1%80%D1%96%D0%B7%D0%B0%D0%BD%D0%B8%D0%B9_%D1%82%D0%B5%D1%82%D1%80%D0%B0%D0%B5%D0%B4%D1%80" title="Зрізаний тетраедр – Ukrainian" lang="uk" hreflang="uk" data-title="Зрізаний тетраедр" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%88%AA%E8%A7%92%E5%9B%9B%E9%9D%A2%E9%AB%94" title="截角四面體 – Chinese" lang="zh" 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<div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Archimedean solid with 8 faces</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox"><tbody><tr><th colspan="2" class="infobox-above" style="background:#e7dcc3">Truncated tetrahedron</th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Afgeknotte_driezijdige_piramide.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Afgeknotte_driezijdige_piramide.png/220px-Afgeknotte_driezijdige_piramide.png" decoding="async" width="220" height="234" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Afgeknotte_driezijdige_piramide.png/330px-Afgeknotte_driezijdige_piramide.png 1.5x, //upload.wikimedia.org/wikipedia/commons/3/3a/Afgeknotte_driezijdige_piramide.png 2x" data-file-width="424" data-file-height="451" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Type</th><td class="infobox-data"><a href="/wiki/Archimedean_solid" title="Archimedean solid">Archimedean solid</a>,<br /><a href="/wiki/Uniform_polyhedron" title="Uniform polyhedron">Uniform polyhedron</a>,<br /><a href="/wiki/Goldberg_polyhedron" title="Goldberg polyhedron">Goldberg polyhedron</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Face_(geometry)" title="Face (geometry)">Faces</a></th><td class="infobox-data">4 <a href="/wiki/Hexagon" title="Hexagon">hexagons</a><br />4 <a href="/wiki/Triangle" title="Triangle">triangles</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Edge_(geometry)" title="Edge (geometry)">Edges</a></th><td class="infobox-data">18</td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Vertex_(geometry)" title="Vertex (geometry)">Vertices</a></th><td class="infobox-data">12</td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/List_of_spherical_symmetry_groups" title="List of spherical symmetry groups">Symmetry group</a></th><td class="infobox-data"><a href="/wiki/Tetrahedral_symmetry" title="Tetrahedral symmetry">tetrahedral symmetry</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {T} _{\mathrm {h} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">T</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">h</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {T} _{\mathrm {h} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4341172931a51303ace861a83995e9231f6c253" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.824ex; height:2.509ex;" alt="{\displaystyle \mathrm {T} _{\mathrm {h} }}" /></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Dual_polyhedron" title="Dual polyhedron">Dual polyhedron</a></th><td class="infobox-data"><a href="/wiki/Triakis_tetrahedron" title="Triakis tetrahedron">triakis tetrahedron</a></td></tr><tr><th colspan="2" class="infobox-header" style="background:#e7dcc3"><a href="/wiki/Vertex_figure" title="Vertex figure">Vertex figure</a></th></tr><tr><td colspan="2" class="infobox-full-data"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Polyhedron_truncated_4a_vertfig.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Polyhedron_truncated_4a_vertfig.svg/250px-Polyhedron_truncated_4a_vertfig.svg.png" decoding="async" width="180" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Polyhedron_truncated_4a_vertfig.svg/330px-Polyhedron_truncated_4a_vertfig.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Polyhedron_truncated_4a_vertfig.svg/360px-Polyhedron_truncated_4a_vertfig.svg.png 2x" data-file-width="340" data-file-height="340" /></a></span></td></tr><tr><th colspan="2" class="infobox-header" style="background:#e7dcc3"><a href="/wiki/Net_(polyhedron)" title="Net (polyhedron)">Net</a></th></tr><tr><td colspan="2" class="infobox-full-data"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Polyhedron_truncated_4a_net.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Polyhedron_truncated_4a_net.svg/280px-Polyhedron_truncated_4a_net.svg.png" decoding="async" width="280" height="222" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Polyhedron_truncated_4a_net.svg/420px-Polyhedron_truncated_4a_net.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/07/Polyhedron_truncated_4a_net.svg/560px-Polyhedron_truncated_4a_net.svg.png 2x" data-file-width="330" data-file-height="262" /></a></span></td></tr></tbody></table> <p>In <a href="/wiki/Geometry" title="Geometry">geometry</a>, the <b>truncated tetrahedron</b> is an <a href="/wiki/Archimedean_solid" title="Archimedean solid">Archimedean solid</a>. It has 4 regular <a href="/wiki/Hexagon" title="Hexagon">hexagonal</a> faces, 4 <a href="/wiki/Equilateral_triangle" title="Equilateral triangle">equilateral triangle</a> faces, 12 vertices and 18 edges (of two types). It can be constructed by <a href="/wiki/Truncation_(geometry)" title="Truncation (geometry)">truncating</a> all 4 vertices of a regular <a href="/wiki/Tetrahedron" title="Tetrahedron">tetrahedron</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Construction">Construction</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truncated_tetrahedron&action=edit&section=1" title="Edit section: Construction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The truncated tetrahedron can be constructed from a <a href="/wiki/Regular_tetrahedron" class="mw-redirect" title="Regular tetrahedron">regular tetrahedron</a> by cutting all of its vertices off, a process known as <a href="/wiki/Truncation_(geometry)" title="Truncation (geometry)">truncation</a>.<sup id="cite_ref-kuchel_1-0" class="reference"><a href="#cite_note-kuchel-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The resulting polyhedron has 4 equilateral triangles and 4 regular hexagons, 18 edges, and 12 vertices.<sup id="cite_ref-berman_2-0" class="reference"><a href="#cite_note-berman-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> With edge length 1, the <a href="/wiki/Cartesian_coordinates" class="mw-redirect" title="Cartesian coordinates">Cartesian coordinates</a> of the 12 vertices are points </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bigl (}{\pm {\tfrac {3{\sqrt {2}}}{4}}},\pm {\tfrac {\sqrt {2}}{4}},\pm {\tfrac {\sqrt {2}}{4}}{\bigr )}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>±</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mrow> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mrow> <mn>4</mn> </mfrac> </mstyle> </mrow> </mrow> <mo>,</mo> <mo>±</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <msqrt> <mn>2</mn> </msqrt> <mn>4</mn> </mfrac> </mstyle> </mrow> <mo>,</mo> <mo>±</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <msqrt> <mn>2</mn> </msqrt> <mn>4</mn> </mfrac> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bigl (}{\pm {\tfrac {3{\sqrt {2}}}{4}}},\pm {\tfrac {\sqrt {2}}{4}},\pm {\tfrac {\sqrt {2}}{4}}{\bigr )}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81939e56b2edc864105f844a276a6e08124cde75" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:19.525ex; height:4.176ex;" alt="{\displaystyle {\bigl (}{\pm {\tfrac {3{\sqrt {2}}}{4}}},\pm {\tfrac {\sqrt {2}}{4}},\pm {\tfrac {\sqrt {2}}{4}}{\bigr )}}" /></span> </p><p>that have an even number of minus signs. </p> <div class="mw-heading mw-heading2"><h2 id="Properties">Properties</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truncated_tetrahedron&action=edit&section=2" title="Edit section: Properties"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Given the edge length <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}" /></span>. The surface area of a truncated tetrahedron <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" /></span> is the sum of 4 regular hexagons and 4 equilateral triangles' area, and its <a href="/wiki/Volume" title="Volume">volume</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}" /></span> is:<sup id="cite_ref-berman_2-1" class="reference"><a href="#cite_note-berman-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}A&=7{\sqrt {3}}a^{2}&&\approx 12.124a^{2},\\V&={\tfrac {23}{12}}{\sqrt {2}}a^{3}&&\approx 2.711a^{3}.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>A</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mn>7</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> <mtd></mtd> <mtd> <mi></mi> <mo>≈</mo> <mn>12.124</mn> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>V</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>23</mn> <mn>12</mn> </mfrac> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mtd> <mtd></mtd> <mtd> <mi></mi> <mo>≈</mo> <mn>2.711</mn> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}A&=7{\sqrt {3}}a^{2}&&\approx 12.124a^{2},\\V&={\tfrac {23}{12}}{\sqrt {2}}a^{3}&&\approx 2.711a^{3}.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d48c89c3595fc7c91bd9a7f264e9a1cf03f36c4" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:30.633ex; height:6.843ex;" alt="{\displaystyle {\begin{aligned}A&=7{\sqrt {3}}a^{2}&&\approx 12.124a^{2},\\V&={\tfrac {23}{12}}{\sqrt {2}}a^{3}&&\approx 2.711a^{3}.\end{aligned}}}" /></span> </p><p>The dihedral angle of a truncated tetrahedron between triangle-to-hexagon is approximately 109.47°, and that between adjacent hexagonal faces is approximately 70.53°.<sup id="cite_ref-johnson_3-0" class="reference"><a href="#cite_note-johnson-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>The densest packing of the truncated tetrahedron is believed to be <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \Phi ={\frac {207}{208}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>207</mn> <mn>208</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \Phi ={\frac {207}{208}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a24361e2f167845490ceb7acff748ea90461fbc1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:8.079ex; height:3.843ex;" alt="{\textstyle \Phi ={\frac {207}{208}}}" /></span>, as reported by two independent groups using <a href="/wiki/Monte_Carlo_methods" class="mw-redirect" title="Monte Carlo methods">Monte Carlo methods</a> by <a href="#CITEREFDamascenoEngelGlotzer2012">Damasceno, Engel & Glotzer (2012)</a> and <a href="#CITEREFJiaoTorquato2013">Jiao & Torquato (2013)</a><span class="error harv-error" style="display: none; font-size:100%"> harvtxt error: no target: CITEREFJiaoTorquato2013 (<a href="/wiki/Category:Harv_and_Sfn_template_errors" title="Category:Harv and Sfn template errors">help</a>)</span>.<sup id="cite_ref-damasceno_4-0" class="reference"><a href="#cite_note-damasceno-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-jiao_5-0" class="reference"><a href="#cite_note-jiao-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Although no mathematical proof exists that this is the best possible packing for the truncated tetrahedron, the high proximity to the unity and independence of the findings make it unlikely that an even denser packing is to be found. If the truncation of the corners is slightly smaller than that of a truncated tetrahedron, this new shape can be used to fill space completely.<sup id="cite_ref-damasceno_4-1" class="reference"><a href="#cite_note-damasceno-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><span class="mw-3d-wrapper" data-label="3D"><a href="/wiki/File:Truncated_tetrahedron.stl" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Truncated_tetrahedron.stl/250px-Truncated_tetrahedron.stl.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Truncated_tetrahedron.stl/330px-Truncated_tetrahedron.stl.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/13/Truncated_tetrahedron.stl/500px-Truncated_tetrahedron.stl.png 2x" data-file-width="5120" data-file-height="2880" /></a></span><figcaption>3D model of a truncated tetrahedron</figcaption></figure> <p>The truncated tetrahedron is an <a href="/wiki/Archimedean_solid" title="Archimedean solid">Archimedean solid</a>, meaning it is a highly symmetric and semi-regular polyhedron, and two or more different <a href="/wiki/Regular_polygon" title="Regular polygon">regular polygonal</a> faces meet in a vertex.<sup id="cite_ref-diudea_6-0" class="reference"><a href="#cite_note-diudea-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> The truncated tetrahedron has the same <a href="/wiki/Point_groups_in_three_dimensions" title="Point groups in three dimensions">three-dimensional group symmetry</a> as the regular tetrahedron, the <a href="/wiki/Tetrahedral_symmetry" title="Tetrahedral symmetry">tetrahedral symmetry</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {T} _{\mathrm {h} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">T</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">h</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {T} _{\mathrm {h} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4341172931a51303ace861a83995e9231f6c253" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.824ex; height:2.509ex;" alt="{\displaystyle \mathrm {T} _{\mathrm {h} }}" /></span>.<sup id="cite_ref-kocakoca_7-0" class="reference"><a href="#cite_note-kocakoca-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> The polygonal faces that meet for every vertex are one equilateral triangle and two regular hexagons, and the <a href="/wiki/Vertex_figure" title="Vertex figure">vertex figure</a> is denoted as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3\cdot 6^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3</mn> <mo>⋅</mo> <msup> <mn>6</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3\cdot 6^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b06007aed3e452fdcb8f481f5d51c45251b75a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.058ex; height:2.676ex;" alt="{\displaystyle 3\cdot 6^{2}}" /></span>. Its <a href="/wiki/Dual_polyhedron" title="Dual polyhedron">dual polyhedron</a> is <a href="/wiki/Triakis_tetrahedron" title="Triakis tetrahedron">triakis tetrahedron</a>, a <a href="/wiki/Catalan_solid" title="Catalan solid">Catalan solid</a>, shares the same symmetry as the truncated tetrahedron.<sup id="cite_ref-williams_8-0" class="reference"><a href="#cite_note-williams-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Related_polyhedrons">Related polyhedrons</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truncated_tetrahedron&action=edit&section=3" title="Edit section: Related polyhedrons"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The truncated tetrahedron can be found in the construction of polyhedrons. For example, the <a href="/wiki/Augmented_truncated_tetrahedron" title="Augmented truncated tetrahedron">augmented truncated tetrahedron</a> is a <a href="/wiki/Johnson_solid" title="Johnson solid">Johnson solid</a> constructed from a truncated tetrahedron by attaching <a href="/wiki/Triangular_cupola" title="Triangular cupola">triangular cupola</a> onto its hexagonal face.<sup id="cite_ref-rajwade_9-0" class="reference"><a href="#cite_note-rajwade-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Triakis_truncated_tetrahedron" title="Triakis truncated tetrahedron">triakis truncated tetrahedron</a> is a polyhedron constructed from a truncated tetrahedron by adding three tetrahedrons onto its triangular faces, as interpreted by the name "<a href="/wiki/Conway_kis_operator" class="mw-redirect" title="Conway kis operator">triakis</a>". It is classified as <a href="/wiki/Plesiohedron" title="Plesiohedron">plesiohedron</a>, meaning it can <a href="/wiki/Tessellation" title="Tessellation">tessellate</a> in three-dimensional space known as <a href="/wiki/Honeycomb_(geometry)" title="Honeycomb (geometry)">honeycomb</a>; an example is <a href="/wiki/Triakis_truncated_tetrahedral_honeycomb" title="Triakis truncated tetrahedral honeycomb">triakis truncated tetrahedral honeycomb</a>.<sup id="cite_ref-grunbaum_10-0" class="reference"><a href="#cite_note-grunbaum-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Truncated_triakis_tetrahedron.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Truncated_triakis_tetrahedron.gif/150px-Truncated_triakis_tetrahedron.gif" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Truncated_triakis_tetrahedron.gif/225px-Truncated_triakis_tetrahedron.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Truncated_triakis_tetrahedron.gif/300px-Truncated_triakis_tetrahedron.gif 2x" data-file-width="600" data-file-height="600" /></a><figcaption>Truncated triakis tetrahedron</figcaption></figure> <p>A <a href="/wiki/Truncated_triakis_tetrahedron" title="Truncated triakis tetrahedron">truncated triakis tetrahedron</a> is known for its usage in chemistry as a <a href="/wiki/Fullerene" title="Fullerene">fullerene</a>. This solid is represented as an <a href="/wiki/Allotrope" class="mw-redirect" title="Allotrope">allotrope</a> of carbon (C<sub>28</sub>), forming the smallest stable fullerene,<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> and experiments have found it to be stabilized by encapsulating a metal atom.<sup id="cite_ref-dkm_12-0" class="reference"><a href="#cite_note-dkm-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Geometrically, this polyhedron was studied in 1935 by Michael Goldberg as a possible solution to the <a href="/wiki/Isoperimetric_problem" class="mw-redirect" title="Isoperimetric problem">isoperimetric problem</a> of maximizing the volume for a given number of faces (16 in this case) and a given surface area.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> For this optimization problem, the optimal geometric form for the polyhedron is one in which the faces are all tangent to an <a href="/wiki/Inscribed_sphere" title="Inscribed sphere">inscribed sphere</a>.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p><span class="anchor" id="Friauf_polyhedron"></span>The <i>Friauf polyhedron</i> is named after <a href="/wiki/J._B._Friauf" class="mw-redirect" title="J. B. Friauf">J. B. Friauf</a> in which he described it as a <a href="/wiki/Intermetallic" title="Intermetallic">intermetallic</a> structure formed by a compound of metallic elements.<sup id="cite_ref-friauf_15-0" class="reference"><a href="#cite_note-friauf-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> It can be found in crystals such as complex metallic alloys, an example is dizinc magnesium MgZn<sub>2</sub>.<sup id="cite_ref-lcd_16-0" class="reference"><a href="#cite_note-lcd-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> It is a lower symmetry version of the truncated tetrahedron, interpreted as a truncated <a href="/wiki/Tetragonal_disphenoid" class="mw-redirect" title="Tetragonal disphenoid">tetragonal disphenoid</a> with its three-dimensional symmetry group as the <a href="/wiki/Dihedral_group" title="Dihedral group">dihedral group</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{2\mathrm {d} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{2\mathrm {d} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10a8beadee2534269537a35765054c7050cb6af7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.892ex; height:2.509ex;" alt="{\displaystyle D_{2\mathrm {d} }}" /></span> of order 8.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2024)">citation needed</span></a></i>]</sup> </p><p>Truncating a truncated tetrahedron gives the resulting polyhedron 54 edges, 32 vertices, and 20 faces—4 hexagons, 4 <a href="/wiki/Nonagon" title="Nonagon">nonagons</a>, and 12 <a href="/wiki/Trapezoid" title="Trapezoid">trapeziums</a>. This polyhedron was used by <a href="/wiki/Adidas" title="Adidas">Adidas</a> as the underlying geometry of the <a href="/wiki/Adidas_Jabulani" title="Adidas Jabulani">Jabulani ball</a> designed for the <a href="/wiki/FIFA_World_Cup_2010" class="mw-redirect" title="FIFA World Cup 2010">2010 World Cup</a>.<sup id="cite_ref-kuchel_1-1" class="reference"><a href="#cite_note-kuchel-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Truncated_tetrahedral_graph">Truncated tetrahedral graph</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truncated_tetrahedron&action=edit&section=4" title="Edit section: Truncated tetrahedral graph"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Tuncated_tetrahedral_graph.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Tuncated_tetrahedral_graph.png/240px-Tuncated_tetrahedral_graph.png" decoding="async" width="240" height="215" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Tuncated_tetrahedral_graph.png/360px-Tuncated_tetrahedral_graph.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Tuncated_tetrahedral_graph.png/480px-Tuncated_tetrahedral_graph.png 2x" data-file-width="521" data-file-height="466" /></a><figcaption>The graph of a truncated tetrahedron</figcaption></figure> <p>In the <a href="/wiki/Mathematics" title="Mathematics">mathematical</a> field of <a href="/wiki/Graph_theory" title="Graph theory">graph theory</a>, a <b>truncated tetrahedral graph</b> is an <a href="/wiki/Archimedean_graph" title="Archimedean graph">Archimedean graph</a>, the <a href="/wiki/1-skeleton" class="mw-redirect" title="1-skeleton">graph of vertices and edges</a> of the truncated tetrahedron, one of the <a href="/wiki/Archimedean_solid" title="Archimedean solid">Archimedean solids</a>. It has 12 <a href="/wiki/Vertex_(graph_theory)" title="Vertex (graph theory)">vertices</a> and 18 edges.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> It is a connected cubic graph,<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> and connected cubic transitive graph.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Truncated_tetrahedron&action=edit&section=5" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul class="gallery mw-gallery-traditional center"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:De_divina_proportione_-_Tetraedron_Abscisum_Vacuum.jpg" class="mw-file-description" title="drawing in De divina proportione (1509)"><img alt="drawing in De divina proportione (1509)" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/De_divina_proportione_-_Tetraedron_Abscisum_Vacuum.jpg/120px-De_divina_proportione_-_Tetraedron_Abscisum_Vacuum.jpg" decoding="async" width="120" height="119" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/De_divina_proportione_-_Tetraedron_Abscisum_Vacuum.jpg/180px-De_divina_proportione_-_Tetraedron_Abscisum_Vacuum.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/31/De_divina_proportione_-_Tetraedron_Abscisum_Vacuum.jpg/240px-De_divina_proportione_-_Tetraedron_Abscisum_Vacuum.jpg 2x" data-file-width="1333" data-file-height="1321" /></a></span></div> <div class="gallerytext"> drawing in <a href="/wiki/De_divina_proportione" class="mw-redirect" title="De divina proportione">De divina proportione</a> (1509)</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Perspectiva_Corporum_Regularium_09a.jpg" class="mw-file-description" title="drawing in Perspectiva Corporum Regularium (1568)"><img alt="drawing in Perspectiva Corporum Regularium (1568)" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Perspectiva_Corporum_Regularium_09a.jpg/120px-Perspectiva_Corporum_Regularium_09a.jpg" decoding="async" width="120" height="118" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Perspectiva_Corporum_Regularium_09a.jpg/180px-Perspectiva_Corporum_Regularium_09a.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/02/Perspectiva_Corporum_Regularium_09a.jpg/240px-Perspectiva_Corporum_Regularium_09a.jpg 2x" data-file-width="610" data-file-height="602" /></a></span></div> <div class="gallerytext"> drawing in <a href="/wiki/Perspectiva_Corporum_Regularium" class="mw-redirect" title="Perspectiva Corporum Regularium">Perspectiva Corporum Regularium</a> (1568)</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Modell,_Kristallform_(Verzerrungen)_Oktaeder_(Spinell)_-Krantz_4,_6,_7,_391-_(8).jpg" class="mw-file-description" title="crystal model"><img alt="crystal model" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/Modell%2C_Kristallform_%28Verzerrungen%29_Oktaeder_%28Spinell%29_-Krantz_4%2C_6%2C_7%2C_391-_%288%29.jpg/120px-Modell%2C_Kristallform_%28Verzerrungen%29_Oktaeder_%28Spinell%29_-Krantz_4%2C_6%2C_7%2C_391-_%288%29.jpg" decoding="async" width="120" height="115" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/Modell%2C_Kristallform_%28Verzerrungen%29_Oktaeder_%28Spinell%29_-Krantz_4%2C_6%2C_7%2C_391-_%288%29.jpg/180px-Modell%2C_Kristallform_%28Verzerrungen%29_Oktaeder_%28Spinell%29_-Krantz_4%2C_6%2C_7%2C_391-_%288%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/86/Modell%2C_Kristallform_%28Verzerrungen%29_Oktaeder_%28Spinell%29_-Krantz_4%2C_6%2C_7%2C_391-_%288%29.jpg/240px-Modell%2C_Kristallform_%28Verzerrungen%29_Oktaeder_%28Spinell%29_-Krantz_4%2C_6%2C_7%2C_391-_%288%29.jpg 2x" data-file-width="1853" data-file-height="1781" /></a></span></div> <div class="gallerytext"> <a href="/wiki/Crystal_model" title="Crystal model">crystal model</a></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Tetraedro_truncado_(Matemateca_IME-USP).jpg" class="mw-file-description" title="photos from different perspectives (Matemateca)"><img alt="photos from different perspectives (Matemateca)" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Tetraedro_truncado_%28Matemateca_IME-USP%29.jpg/120px-Tetraedro_truncado_%28Matemateca_IME-USP%29.jpg" decoding="async" width="120" height="55" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Tetraedro_truncado_%28Matemateca_IME-USP%29.jpg/250px-Tetraedro_truncado_%28Matemateca_IME-USP%29.jpg 1.5x" data-file-width="18750" data-file-height="8547" /></a></span></div> <div class="gallerytext"> photos from different perspectives (<a href="/wiki/Matemateca" title="Matemateca">Matemateca</a>)</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:D4_truncated_tetrahedron.JPG" class="mw-file-description" title="4-sided die"><img alt="4-sided die" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/D4_truncated_tetrahedron.JPG/119px-D4_truncated_tetrahedron.JPG" decoding="async" width="119" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/D4_truncated_tetrahedron.JPG/178px-D4_truncated_tetrahedron.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/36/D4_truncated_tetrahedron.JPG/238px-D4_truncated_tetrahedron.JPG 2x" data-file-width="699" data-file-height="705" /></a></span></div> <div class="gallerytext"> 4-sided <a href="/wiki/Dice#Polyhedral_dice" title="Dice">die</a></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Permutohedron_in_simplex_of_order_4,_with_truncated_tetrahedron_(0-based).png" class="mw-file-description" title="12 permutations of '"`UNIQ--postMath-0000000B-QINU`"' (brown)"><img alt="12 permutations of '"`UNIQ--postMath-0000000B-QINU`"' (brown)" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Permutohedron_in_simplex_of_order_4%2C_with_truncated_tetrahedron_%280-based%29.png/112px-Permutohedron_in_simplex_of_order_4%2C_with_truncated_tetrahedron_%280-based%29.png" decoding="async" width="112" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Permutohedron_in_simplex_of_order_4%2C_with_truncated_tetrahedron_%280-based%29.png/168px-Permutohedron_in_simplex_of_order_4%2C_with_truncated_tetrahedron_%280-based%29.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Permutohedron_in_simplex_of_order_4%2C_with_truncated_tetrahedron_%280-based%29.png/224px-Permutohedron_in_simplex_of_order_4%2C_with_truncated_tetrahedron_%280-based%29.png 2x" data-file-width="3740" data-file-height="4000" /></a></span></div> <div class="gallerytext"> 12 <a href="/wiki/Permutations#Permutations_of_multisets" class="mw-redirect" title="Permutations">permutations</a> of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (4,2,0,0)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>4</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (4,2,0,0)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9522ada57931b87c929e218acb20a6e13bccee6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.561ex; height:2.843ex;" alt="{\displaystyle (4,2,0,0)}" /></span> (brown)</div> </li> </ul> <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=Truncated_tetrahedron&action=edit&section=6" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Quarter_cubic_honeycomb" title="Quarter cubic honeycomb">Quarter cubic honeycomb</a> – Fills space using truncated tetrahedra and smaller tetrahedra</li> <li><a href="/wiki/Truncated_5-cell" title="Truncated 5-cell">Truncated 5-cell</a> – Similar uniform polytope in 4-dimensions</li> <li><a href="/wiki/Truncated_triakis_tetrahedron" title="Truncated triakis tetrahedron">Truncated triakis tetrahedron</a></li> <li><a href="/wiki/Triakis_truncated_tetrahedron" title="Triakis truncated tetrahedron">Triakis truncated tetrahedron</a></li> <li><a href="/wiki/Octahedron" title="Octahedron">Octahedron</a> – a rectified tetrahedron</li> <li><a href="/wiki/Truncated_Triangular_Pyramid_Number" class="mw-redirect" title="Truncated Triangular Pyramid Number">Truncated Triangular Pyramid Number</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=Truncated_tetrahedron&action=edit&section=7" 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 mw-references-columns"><ol class="references"> <li id="cite_note-kuchel-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-kuchel_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-kuchel_1-1"><sup><i><b>b</b></i></sup></a></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 id="CITEREFKuchel2012" class="citation journal cs1">Kuchel, Philip W. 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"96.45 Can you 'bend' a truncated truncated tetrahedron?". <i><a href="/wiki/The_Mathematical_Gazette" title="The Mathematical Gazette">The Mathematical Gazette</a></i>. <b>96</b> (536): <span class="nowrap">317–</span>323. <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%2FS0025557200004666">10.1017/S0025557200004666</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/23248575">23248575</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Mathematical+Gazette&rft.atitle=96.45+Can+you+%27bend%27+a+truncated+truncated+tetrahedron%3F&rft.volume=96&rft.issue=536&rft.pages=%3Cspan+class%3D%22nowrap%22%3E317-%3C%2Fspan%3E323&rft.date=2012&rft_id=info%3Adoi%2F10.1017%2FS0025557200004666&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F23248575%23id-name%3DJSTOR&rft.aulast=Kuchel&rft.aufirst=Philip+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATruncated+tetrahedron" class="Z3988"></span></span> </li> <li id="cite_note-berman-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-berman_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-berman_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBerman1971" class="citation journal cs1">Berman, Martin (1971). 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C.; Wilson, R. J. (1998), <i>An Atlas of Graphs</i>, Oxford University Press</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Atlas+of+Graphs&rft.pub=Oxford+University+Press&rft.date=1998&rft.aulast=Read&rft.aufirst=R.+C.&rft.au=Wilson%2C+R.+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATruncated+tetrahedron" class="Z3988"></span></li></ul> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/60px-Commons-logo.svg.png 1.5x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Truncated_tetrahedron" class="extiw" title="commons:Category:Truncated tetrahedron">Truncated tetrahedron</a></span>.</div></div> </div> <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=Truncated_tetrahedron&action=edit&section=8" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite id="Reference-Mathworld-Truncated_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/TruncatedTetrahedron.html">Truncated tetrahedron</a>" ("<a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/ArchimedeanSolid.html">Archimedean solid</a>") at <i><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></i>.</cite> <ul><li><span class="citation mathworld" id="Reference-Mathworld-Truncated_tetrahedral_graph"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWeisstein" class="citation web cs1"><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/TruncatedTetrahedralGraph.html">"Truncated tetrahedral graph"</a>. <i><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MathWorld&rft.atitle=Truncated+tetrahedral+graph&rft.au=Weisstein%2C+Eric+W.&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FTruncatedTetrahedralGraph.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATruncated+tetrahedron" class="Z3988"></span></span></li></ul></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKlitzing" class="citation web cs1">Klitzing, Richard. <a rel="nofollow" class="external text" href="https://bendwavy.org/klitzing/dimensions/polyhedra.htm">"3D convex uniform polyhedra x3x3o - tut"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=3D+convex+uniform+polyhedra+x3x3o+-+tut&rft.aulast=Klitzing&rft.aufirst=Richard&rft_id=https%3A%2F%2Fbendwavy.org%2Fklitzing%2Fdimensions%2Fpolyhedra.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATruncated+tetrahedron" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://www.dr-mikes-math-games-for-kids.com/polyhedral-nets.html?net=3cqTmfu7gdEZ8I7kRUVvji6qxBATVSp2WpmIWGx7l7pWe7bveylFxv3piHnPNZN&name=Truncated+Tetrahedron#applet">Editable printable net of a truncated tetrahedron with interactive 3D view</a></li> <li><a rel="nofollow" class="external text" href="http://www.mathconsult.ch/showroom/unipoly/">The Uniform Polyhedra</a></li> <li><a rel="nofollow" class="external text" href="http://www.georgehart.com/virtual-polyhedra/vp.html">Virtual Reality Polyhedra</a> The Encyclopedia of Polyhedra</li></ul> <div class="navbox-styles"><style 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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_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 class="mw-selflink selflink">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 class="mw-selflink selflink">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" style="opacity: .4;"><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/250px-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/330px-Polyhedron_4-4.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/66/Polyhedron_4-4.png/500px-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" style="opacity: .4;"><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/120px-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/250px-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/120px-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/250px-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> <tr> <td colspan="8"> <div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Catalan_duals31" 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="Catalan_duals31" style="font-size:114%;margin:0 4em"><a href="/wiki/Catalan_solid" title="Catalan solid">Catalan</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_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 href="/wiki/Triakis_tetrahedron" title="Triakis tetrahedron">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 href="/wiki/Triakis_tetrahedron" title="Triakis tetrahedron">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/120px-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/250px-Polyhedron_truncated_20_dual.png 1.5x" 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" style="opacity: .4;"><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/250px-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/330px-Polyhedron_4-4_dual.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/74/Polyhedron_4-4_dual.png/500px-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/120px-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/250px-Polyhedron_small_rhombi_12-20_dual_max.png 1.5x" 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" style="opacity: .4;"><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/120px-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/250px-Polyhedron_snub_4-4_right_dual_max.png 1.5x" 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/120px-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/250px-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></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_polyhedra686" 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_polyhedra686" 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 class="mw-selflink selflink">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 href="/wiki/Triakis_tetrahedron" title="Triakis tetrahedron">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 class="navbox-abovebelow" colspan="2"><div>Degenerate polyhedra are in <i>italics</i>.</div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" 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