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<span>Dimensions</span> </div> </a> <ul id="toc-Dimensions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Geometric_relations" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Geometric_relations"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Geometric relations</span> </div> </a> <ul id="toc-Geometric_relations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cartesian_coordinates" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Cartesian_coordinates"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Cartesian coordinates</span> </div> </a> <ul id="toc-Cartesian_coordinates-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Orthogonal_projections" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Orthogonal_projections"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Orthogonal projections</span> </div> </a> <ul id="toc-Orthogonal_projections-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Spherical_tiling" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Spherical_tiling"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Spherical tiling</span> </div> </a> <ul id="toc-Spherical_tiling-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Related_polyhedra" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Related_polyhedra"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Related polyhedra</span> </div> </a> <button aria-controls="toc-Related_polyhedra-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Related polyhedra subsection</span> </button> <ul id="toc-Related_polyhedra-sublist" class="vector-toc-list"> <li id="toc-Symmetry_mutations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Symmetry_mutations"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Symmetry mutations</span> </div> </a> <ul id="toc-Symmetry_mutations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Johnson_solids" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Johnson_solids"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Johnson solids</span> </div> </a> <ul id="toc-Johnson_solids-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vertex_arrangement" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Vertex_arrangement"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.3</span> <span>Vertex arrangement</span> </div> </a> <ul id="toc-Vertex_arrangement-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Rhombicosidodecahedral_graph" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Rhombicosidodecahedral_graph"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Rhombicosidodecahedral graph</span> </div> </a> <ul id="toc-Rhombicosidodecahedral_graph-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header 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</div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Rhombicosidodecahedron</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. 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%A0%D0%BE%D0%BC%D0%B1%D0%B8%D0%BA%D0%BE%D1%81%D0%B8%D0%B4%D0%BE%D0%B4%D0%B5%D0%BA%D0%B0%D0%B5%D0%B4%D1%8A%D1%80" title="Ромбикосидодекаедър – Bulgarian" lang="bg" hreflang="bg" data-title="Ромбикосидодекаедър" 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/Rombicosidodec%C3%A0edre" title="Rombicosidodecàedre – Catalan" lang="ca" hreflang="ca" data-title="Rombicosidodecàedre" 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/Rhombenikosidodekaeder" title="Rhombenikosidodekaeder – German" lang="de" hreflang="de" data-title="Rhombenikosidodekaeder" 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%A1%CE%BF%CE%BC%CE%B2%CE%BF%CE%B5%CE%B9%CE%BA%CE%BF%CF%83%CE%B9%CE%B4%CF%89%CE%B4%CE%B5%CE%BA%CE%AC%CE%B5%CE%B4%CF%81%CE%BF" title="Ρομβοεικοσιδωδεκάεδρο – Greek" lang="el" hreflang="el" data-title="Ρομβοεικοσιδωδεκάεδρο" 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/Rombicosidodecaedro" title="Rombicosidodecaedro – Spanish" lang="es" hreflang="es" data-title="Rombicosidodecaedro" 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/Rombo-dudek-dekduedro" title="Rombo-dudek-dekduedro – Esperanto" lang="eo" hreflang="eo" data-title="Rombo-dudek-dekduedro" 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/Erronbikosidodekaedro" title="Erronbikosidodekaedro – Basque" lang="eu" hreflang="eu" data-title="Erronbikosidodekaedro" 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/%D9%84%D9%88%D8%B2%D8%A8%DB%8C%D8%B3%D8%AA%E2%80%8C%D8%AF%D9%88%D8%A7%D8%B2%D8%AF%D9%87%E2%80%8C%D9%88%D8%AC%D9%87%DB%8C" title="لوزبیست‌دوازده‌وجهی – Persian" lang="fa" hreflang="fa" data-title="لوزبیست‌دوازده‌وجهی" 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/Petit_rhombicosidod%C3%A9ca%C3%A8dre" title="Petit rhombicosidodécaèdre – French" lang="fr" hreflang="fr" data-title="Petit rhombicosidodécaèdre" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Rombicosidodecaedro" title="Rombicosidodecaedro – Galician" lang="gl" hreflang="gl" data-title="Rombicosidodecaedro" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%A7%88%EB%A6%84%EB%AA%A8%EC%8B%AD%EC%9D%B4%EC%9D%B4%EC%8B%AD%EB%A9%B4%EC%B2%B4" title="마름모십이이십면체 – Korean" lang="ko" hreflang="ko" data-title="마름모십이이십면체" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Rombikosidodekahedron" title="Rombikosidodekahedron – Indonesian" lang="id" hreflang="id" data-title="Rombikosidodekahedron" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Rombicosidodecaedro" title="Rombicosidodecaedro – Italian" lang="it" hreflang="it" data-title="Rombicosidodecaedro" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Rombische_icosidodeca%C3%ABder" title="Rombische icosidodecaëder – Dutch" lang="nl" hreflang="nl" data-title="Rombische icosidodecaëder" 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/%E6%96%9C%E6%96%B9%E4%BA%8C%E5%8D%81%E3%83%BB%E5%8D%81%E4%BA%8C%E9%9D%A2%E4%BD%93" title="斜方二十・十二面体 – Japanese" lang="ja" hreflang="ja" data-title="斜方二十・十二面体" 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/Rombikosidodekaeder" title="Rombikosidodekaeder – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Rombikosidodekaeder" 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/Rombikosidodekaeder" title="Rombikosidodekaeder – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Rombikosidodekaeder" 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/Dwudziesto-dwunasto%C5%9Bcian_rombowy_ma%C5%82y" title="Dwudziesto-dwunastościan rombowy mały – Polish" lang="pl" hreflang="pl" data-title="Dwudziesto-dwunastościan rombowy mały" 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/Rombicosidodecaedro" title="Rombicosidodecaedro – Portuguese" lang="pt" hreflang="pt" data-title="Rombicosidodecaedro" 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/Rombicosidodecaedru" title="Rombicosidodecaedru – Romanian" lang="ro" hreflang="ro" data-title="Rombicosidodecaedru" 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%A0%D0%BE%D0%BC%D0%B1%D0%BE%D0%B8%D0%BA%D0%BE%D1%81%D0%BE%D0%B4%D0%BE%D0%B4%D0%B5%D0%BA%D0%B0%D1%8D%D0%B4%D1%80" title="Ромбоикосододекаэдр – Russian" lang="ru" hreflang="ru" data-title="Ромбоикосододекаэдр" 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/Rombiikozidodekaeder" title="Rombiikozidodekaeder – Slovenian" lang="sl" hreflang="sl" data-title="Rombiikozidodekaeder" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A3%E0%B8%AD%E0%B8%A1%E0%B8%9A%E0%B8%B4%E0%B9%82%E0%B8%84%E0%B8%8B%E0%B8%B4%E0%B9%82%E0%B8%94%E0%B9%80%E0%B8%94%E0%B8%84%E0%B8%B2%E0%B8%AE%E0%B8%B5%E0%B8%94%E0%B8%A3%E0%B8%AD%E0%B8%99" title="รอมบิโคซิโดเดคาฮีดรอน – Thai" lang="th" hreflang="th" data-title="รอมบิโคซิโดเดคาฮีดรอน" 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%A0%D0%BE%D0%BC%D0%B1%D0%BE%D1%96%D0%BA%D0%BE%D1%81%D0%BE%D0%B4%D0%BE%D0%B4%D0%B5%D0%BA%D0%B0%D0%B5%D0%B4%D1%80" title="Ромбоікосододекаедр – Ukrainian" lang="uk" hreflang="uk" data-title="Ромбоікосододекаедр" 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 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src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Rhombicosidodecahedron.jpg/320px-Rhombicosidodecahedron.jpg" decoding="async" width="320" height="325" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Rhombicosidodecahedron.jpg/480px-Rhombicosidodecahedron.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Rhombicosidodecahedron.jpg/640px-Rhombicosidodecahedron.jpg 2x" data-file-width="858" data-file-height="871" /></a></span><br /><a href="/wiki/File:Rhombicosidodecahedron.gif" title="File:Rhombicosidodecahedron.gif">(Click here for rotating model)</a> </td></tr> <tr> <td style="background-color:#e7dcc3;" width="105">Type</td> <td><a href="/wiki/Archimedean_solid" title="Archimedean solid">Archimedean solid</a><br /><a href="/wiki/Uniform_polyhedron" title="Uniform polyhedron">Uniform polyhedron</a> </td></tr> <tr> <td style="background-color:#e7dcc3;"><a href="/wiki/Euler_characteristic" title="Euler characteristic">Elements</a></td> <td><i>F</i> = 62, <i>E</i> = 120, <i>V</i> = 60 (χ = 2) </td></tr> <tr> <td style="background-color:#e7dcc3;">Faces by sides</td> <td>20{3}+30{4}+12{5} </td></tr> <tr> <td style="background-color:#e7dcc3;"><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">Conway notation</a></td> <td>eD or aaD </td></tr> <tr> <td rowspan="2" style="background-color:#e7dcc3"><a href="/wiki/Schl%C3%A4fli_symbol" title="Schläfli symbol">Schläfli symbols</a></td> <td>rr{5,3} or <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 r{\begin{Bmatrix}5\\3\end{Bmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>5</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> </mtable> <mo>}</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r{\begin{Bmatrix}5\\3\end{Bmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/83b11b3a7728640541021e79254db6567009dc23" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:6.449ex; height:6.176ex;" alt="{\displaystyle r{\begin{Bmatrix}5\\3\end{Bmatrix}}}"></span> </td></tr> <tr> <td>t<sub>0,2</sub>{5,3} </td></tr> <tr> <td style="background-color:#e7dcc3;"><a href="/wiki/Wythoff_symbol" title="Wythoff symbol">Wythoff symbol</a></td> <td>3 5 | 2 </td></tr> <tr> <td style="background-color:#e7dcc3;"><a href="/wiki/Coxeter_diagram" class="mw-redirect" title="Coxeter diagram">Coxeter diagram</a></td> <td><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.png" decoding="async" width="7" height="23" class="mw-file-element" data-file-width="7" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span></span> </td></tr> <tr> <td style="background-color:#e7dcc3;"><a href="/wiki/List_of_spherical_symmetry_groups" title="List of spherical symmetry groups">Symmetry group</a></td> <td><a href="/wiki/Icosahedral_symmetry" title="Icosahedral symmetry">I<sub>h</sub></a>, H<sub>3</sub>, [5,3], (*532), order 120 </td></tr> <tr> <td style="background-color:#e7dcc3;"><a href="/wiki/Point_groups_in_three_dimensions#Rotation_groups" title="Point groups in three dimensions">Rotation group</a></td> <td><a href="/wiki/Icosahedral_symmetry" title="Icosahedral symmetry">I</a>, [5,3]<sup>+</sup>, (532), order 60 </td></tr> <tr> <td style="background-color:#e7dcc3;"><a href="/wiki/Dihedral_angle" title="Dihedral angle">Dihedral angle</a></td> <td>3-4: 159°05′41″ (159.09°)<br />4-5: 148°16′57″ (148.28°) </td></tr> <tr> <td style="background-color:#e7dcc3;"><a href="/wiki/List_of_uniform_polyhedra#Indexing" title="List of uniform polyhedra">References</a></td> <td><a href="/wiki/Uniform_polyhedron" title="Uniform polyhedron">U</a><sub>27</sub>, <a href="/wiki/Harold_Scott_MacDonald_Coxeter" title="Harold Scott MacDonald Coxeter">C</a><sub>30</sub>, <a href="/wiki/List_of_Wenninger_polyhedron_models" title="List of Wenninger polyhedron models">W</a><sub>14</sub> </td></tr> <tr> <td style="background-color:#e7dcc3;">Properties</td> <td>Semiregular <a href="/wiki/Convex_polyhedron" class="mw-redirect" title="Convex polyhedron">convex</a> </td></tr> <tr> <td style="text-align:center;"><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/100px-Polyhedron_small_rhombi_12-20_max.png" decoding="async" width="100" height="101" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Polyhedron_small_rhombi_12-20_max.png/150px-Polyhedron_small_rhombi_12-20_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Polyhedron_small_rhombi_12-20_max.png/200px-Polyhedron_small_rhombi_12-20_max.png 2x" data-file-width="3973" data-file-height="4000" /></a></span><br />Colored faces </td> <td style="vertical-align:top;text-align:center;"><span typeof="mw:File"><a href="/wiki/File:Polyhedron_small_rhombi_12-20_vertfig.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Polyhedron_small_rhombi_12-20_vertfig.svg/140px-Polyhedron_small_rhombi_12-20_vertfig.svg.png" decoding="async" width="140" height="140" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Polyhedron_small_rhombi_12-20_vertfig.svg/210px-Polyhedron_small_rhombi_12-20_vertfig.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/30/Polyhedron_small_rhombi_12-20_vertfig.svg/280px-Polyhedron_small_rhombi_12-20_vertfig.svg.png 2x" data-file-width="375" data-file-height="375" /></a></span><br />3.4.5.4<br />(<a href="/wiki/Vertex_figure" title="Vertex figure">Vertex figure</a>) </td></tr> <tr> <td style="vertical-align:top;text-align:center;"><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/100px-Polyhedron_small_rhombi_12-20_dual_max.png" decoding="async" width="100" height="99" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Polyhedron_small_rhombi_12-20_dual_max.png/150px-Polyhedron_small_rhombi_12-20_dual_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/28/Polyhedron_small_rhombi_12-20_dual_max.png/200px-Polyhedron_small_rhombi_12-20_dual_max.png 2x" data-file-width="3954" data-file-height="3911" /></a></span><br /><a href="/wiki/Deltoidal_hexecontahedron" title="Deltoidal hexecontahedron">Deltoidal hexecontahedron</a><br />(<a href="/wiki/Dual_polyhedron" title="Dual polyhedron">dual polyhedron</a>) </td> <td style="text-align:center;"><span typeof="mw:File"><a href="/wiki/File:Polyhedron_small_rhombi_12-20_net.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/Polyhedron_small_rhombi_12-20_net.svg/140px-Polyhedron_small_rhombi_12-20_net.svg.png" decoding="async" width="140" height="111" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/Polyhedron_small_rhombi_12-20_net.svg/210px-Polyhedron_small_rhombi_12-20_net.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/36/Polyhedron_small_rhombi_12-20_net.svg/280px-Polyhedron_small_rhombi_12-20_net.svg.png 2x" data-file-width="512" data-file-height="407" /></a></span><br /><a href="/wiki/Net_(polyhedron)" title="Net (polyhedron)">Net</a> </td></tr></tbody></table> <p>In <a href="/wiki/Geometry" title="Geometry">geometry</a>, the <b>rhombicosidodecahedron</b> is an <a href="/wiki/Archimedean_solid" title="Archimedean solid">Archimedean solid</a>, one of thirteen <a href="/wiki/Convex_polyhedron" class="mw-redirect" title="Convex polyhedron">convex</a> <a href="/wiki/Isogonal_figure" title="Isogonal figure">isogonal</a> nonprismatic solids constructed of two or more types of <a href="/wiki/Regular_polygon" title="Regular polygon">regular polygon</a> <a href="/wiki/Face_(geometry)" title="Face (geometry)">faces</a>. </p><p>It has 20 regular <a href="/wiki/Triangular" class="mw-redirect" title="Triangular">triangular</a> faces, 30 <a href="/wiki/Square_(geometry)" class="mw-redirect" title="Square (geometry)">square</a> faces, 12 regular <a href="/wiki/Pentagon" title="Pentagon">pentagonal</a> faces, 60 <a href="/wiki/Vertex_(geometry)" title="Vertex (geometry)">vertices</a>, and 120 <a href="/wiki/Edge_(geometry)" title="Edge (geometry)">edges</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Names">Names</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rhombicosidodecahedron&action=edit&section=1" title="Edit section: Names"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1237032888/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti 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img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style><div class="thumb tmulti tleft"><div class="thumbinner multiimageinner" style="width:342px;max-width:342px"><div class="trow"><div class="tsingle" style="width:112px;max-width:112px"><div class="thumbimage" style="height:104px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Nonuniform_rhombicosidodecahedron_as_rectified_rhombic_triacontahedron_max.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Nonuniform_rhombicosidodecahedron_as_rectified_rhombic_triacontahedron_max.png/110px-Nonuniform_rhombicosidodecahedron_as_rectified_rhombic_triacontahedron_max.png" decoding="async" width="110" height="105" class="mw-file-element" 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height="105" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Rhombicosidodecahedron_in_rhombic_triacontahedron_max.png/165px-Rhombicosidodecahedron_in_rhombic_triacontahedron_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Rhombicosidodecahedron_in_rhombic_triacontahedron_max.png/220px-Rhombicosidodecahedron_in_rhombic_triacontahedron_max.png 2x" data-file-width="3811" data-file-height="3636" /></a></span></div></div><div class="tsingle" style="width:112px;max-width:112px"><div class="thumbimage" style="height:104px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Nonuniform_rhombicosidodecahedron_as_core_of_dual_compound_max.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Nonuniform_rhombicosidodecahedron_as_core_of_dual_compound_max.png/110px-Nonuniform_rhombicosidodecahedron_as_core_of_dual_compound_max.png" decoding="async" width="110" height="105" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Nonuniform_rhombicosidodecahedron_as_core_of_dual_compound_max.png/165px-Nonuniform_rhombicosidodecahedron_as_core_of_dual_compound_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Nonuniform_rhombicosidodecahedron_as_core_of_dual_compound_max.png/220px-Nonuniform_rhombicosidodecahedron_as_core_of_dual_compound_max.png 2x" data-file-width="3811" data-file-height="3636" /></a></span></div></div></div></div></div> <p><a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Johannes Kepler</a> in <i><a href="/wiki/Harmonices_Mundi" title="Harmonices Mundi">Harmonices Mundi</a></i> (1618) named this polyhedron a <i>rhombicosidodecahedron</i>, being short for <i>truncated icosidodecahedral rhombus</i>, with <i>icosidodecahedral rhombus</i> being his name for a <a href="/wiki/Rhombic_triacontahedron" title="Rhombic triacontahedron">rhombic triacontahedron</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> There are different truncations of a <a href="/wiki/Rhombic_triacontahedron" title="Rhombic triacontahedron">rhombic triacontahedron</a> into a <a href="/wiki/Topology" title="Topology">topological</a> rhombicosidodecahedron: Prominently its <a href="/wiki/Rectification_(geometry)" title="Rectification (geometry)">rectification</a> (left), the one that creates the uniform solid (center), and the rectification of the dual <a href="/wiki/Icosidodecahedron" title="Icosidodecahedron">icosidodecahedron</a> (right), which is the core of the <a href="/wiki/Dual_compound" class="mw-redirect" title="Dual compound">dual compound</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Dimensions">Dimensions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rhombicosidodecahedron&action=edit&section=2" title="Edit section: Dimensions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For a rhombicosidodecahedron with edge length <i>a</i>, its surface area and volume are: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}A&=\left(30+5{\sqrt {3}}+3{\sqrt {25+10{\sqrt {5}}}}\right)a^{2}&&\approx 59.305\,982\,844\,9a^{2}\\V&={\frac {60+29{\sqrt {5}}}{3}}a^{3}&&\approx 41.615\,323\,782\,5a^{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> <mrow> <mo>(</mo> <mrow> <mn>30</mn> <mo>+</mo> <mn>5</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> <mo>+</mo> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>25</mn> <mo>+</mo> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>5</mn> </msqrt> </mrow> </msqrt> </mrow> </mrow> <mo>)</mo> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> <mtd /> <mtd> <mi></mi> <mo>≈</mo> <mn>59.305</mn> <mspace width="thinmathspace" /> <mn>982</mn> <mspace width="thinmathspace" /> <mn>844</mn> <mspace width="thinmathspace" /> <mn>9</mn> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> </mtr> <mtr> <mtd> <mi>V</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>60</mn> <mo>+</mo> <mn>29</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>5</mn> </msqrt> </mrow> </mrow> <mn>3</mn> </mfrac> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mtd> <mtd /> <mtd> <mi></mi> <mo>≈</mo> <mn>41.615</mn> <mspace width="thinmathspace" /> <mn>323</mn> <mspace width="thinmathspace" /> <mn>782</mn> <mspace width="thinmathspace" /> <mn>5</mn> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}A&=\left(30+5{\sqrt {3}}+3{\sqrt {25+10{\sqrt {5}}}}\right)a^{2}&&\approx 59.305\,982\,844\,9a^{2}\\V&={\frac {60+29{\sqrt {5}}}{3}}a^{3}&&\approx 41.615\,323\,782\,5a^{3}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3dc631fdb4468717967eb4c8f29ebaec30ba684" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.505ex; width:63.856ex; height:12.176ex;" alt="{\displaystyle {\begin{aligned}A&=\left(30+5{\sqrt {3}}+3{\sqrt {25+10{\sqrt {5}}}}\right)a^{2}&&\approx 59.305\,982\,844\,9a^{2}\\V&={\frac {60+29{\sqrt {5}}}{3}}a^{3}&&\approx 41.615\,323\,782\,5a^{3}\end{aligned}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Geometric_relations">Geometric relations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rhombicosidodecahedron&action=edit&section=3" title="Edit section: Geometric relations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>If you <a href="/wiki/Expansion_(geometry)" title="Expansion (geometry)">expand</a> an <a href="/wiki/Icosidodecahedron" title="Icosidodecahedron">icosidodecahedron</a> by moving the faces away from the <a href="/wiki/Origin_(mathematics)" title="Origin (mathematics)">origin</a> the right amount, without changing the orientation or size of the faces, and patch the square holes in the result, you get a rhombicosidodecahedron. Therefore, it has the same number of triangles as an <a href="/wiki/Icosahedron" title="Icosahedron">icosahedron</a> and the same number of pentagons as a <a href="/wiki/Dodecahedron" title="Dodecahedron">dodecahedron</a>, with a square for each edge of either. </p><p>Alternatively, if you <a href="/wiki/Expansion_(geometry)" title="Expansion (geometry)">expand</a> each of five cubes by moving the faces away from the <a href="/wiki/Origin_(mathematics)" title="Origin (mathematics)">origin</a> the right amount and rotating each of the five 72° around so they are equidistant from each other, without changing the orientation or size of the faces, and patch the pentagonal and triangular holes in the result, you get a rhombicosidodecahedron. Therefore, it has the same number of squares as five cubes. </p><p>Two clusters of faces of the <a href="/wiki/Bilunabirotunda" title="Bilunabirotunda">bilunabirotunda</a>, the <i>lunes</i> (each <i>lune</i> featuring two triangles adjacent to opposite sides of one square), can be aligned with a congruent patch of faces on the rhombicosidodecahedron. If two bilunabirotundae are aligned this way on opposite sides of the rhombicosidodecahedron, then a cube can be put between the bilunabirotundae at the very center of the rhombicosidodecahedron. </p><p>The rhombicosidodecahedron shares the vertex arrangement with the <a href="/wiki/Small_stellated_truncated_dodecahedron" title="Small stellated truncated dodecahedron">small stellated truncated dodecahedron</a>, and with the uniform compounds of six or twelve <a href="/wiki/Pentagrammic_prism" title="Pentagrammic prism">pentagrammic prisms</a>. </p><p>The <a href="/wiki/Zometool" title="Zometool">Zometool</a> kits for making <a href="/wiki/Geodesic_dome" title="Geodesic dome">geodesic domes</a> and other <a href="/wiki/Polyhedron" title="Polyhedron">polyhedra</a> use slotted balls as connectors. The balls are "expanded" rhombicosidodecahedra, with the squares replaced by rectangles. The expansion is chosen so that the resulting rectangles are <a href="/wiki/Golden_rectangle" title="Golden rectangle">golden rectangles</a>. </p><p>Twelve of the 92 <a href="/wiki/Johnson_solid" title="Johnson solid">Johnson solids</a> are derived from the rhombicosidodecahedron, four of them by rotation of one or more <a href="/wiki/Pentagonal_cupola" title="Pentagonal cupola">pentagonal cupolae</a>: the <a href="/wiki/Gyrate_rhombicosidodecahedron" title="Gyrate rhombicosidodecahedron">gyrate</a>, <a href="/wiki/Parabigyrate_rhombicosidodecahedron" title="Parabigyrate rhombicosidodecahedron">parabigyrate</a>, <a href="/wiki/Metabigyrate_rhombicosidodecahedron" title="Metabigyrate rhombicosidodecahedron">metabigyrate</a>, and <a href="/wiki/Trigyrate_rhombicosidodecahedron" title="Trigyrate rhombicosidodecahedron">trigyrate rhombicosidodecahedron</a>. Eight more can be constructed by removing up to three cupolae, sometimes also rotating one or more of the other cupolae. </p> <div class="mw-heading mw-heading2"><h2 id="Cartesian_coordinates">Cartesian coordinates</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rhombicosidodecahedron&action=edit&section=4" title="Edit section: Cartesian coordinates"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Cartesian_coordinates" class="mw-redirect" title="Cartesian coordinates">Cartesian coordinates</a> for the vertices of a rhombicosidodecahedron with an edge length of 2 centered at the origin are all <a href="/wiki/Even_permutation" class="mw-redirect" title="Even permutation">even permutations</a> of:<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <dl><dd>(±1, ±1, ±<i>φ</i><sup>3</sup>),</dd> <dd>(±<i>φ</i><sup>2</sup>, ±<i>φ</i>, ±2<i>φ</i>),</dd> <dd>(±(2+<i>φ</i>), 0, ±<i>φ</i><sup>2</sup>),</dd></dl> <p>where <i>φ</i> = <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">1 + <span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">5</span></span></span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> is the <a href="/wiki/Golden_ratio" title="Golden ratio">golden ratio</a>. Therefore, the <a href="/wiki/Circumradius" class="mw-redirect" title="Circumradius">circumradius</a> of this rhombicosidodecahedron is the common distance of these points from the origin, namely <span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;"><i>φ</i><sup>6</sup>+2</span></span> = <span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;"><i>8φ+7</i></span></span> for edge length 2. For unit edge length, R must be halved, giving </p> <dl><dd><i>R</i> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">8<i>φ</i>+7</span></span></span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">11+4<span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">5</span></span></span></span></span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> ≈ 2.233.</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Orthogonal_projections">Orthogonal projections</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rhombicosidodecahedron&action=edit&section=5" title="Edit section: Orthogonal projections"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237032888/mw-parser-output/.tmulti"><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:192px;max-width:192px"><div class="trow"><div class="tsingle" style="width:190px;max-width:190px"><div class="thumbimage" style="height:215px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Houghton_Typ_520.43.454,_crop_solid_and_owl.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Houghton_Typ_520.43.454%2C_crop_solid_and_owl.jpg/188px-Houghton_Typ_520.43.454%2C_crop_solid_and_owl.jpg" decoding="async" width="188" height="215" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Houghton_Typ_520.43.454%2C_crop_solid_and_owl.jpg/282px-Houghton_Typ_520.43.454%2C_crop_solid_and_owl.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/56/Houghton_Typ_520.43.454%2C_crop_solid_and_owl.jpg/376px-Houghton_Typ_520.43.454%2C_crop_solid_and_owl.jpg 2x" data-file-width="802" data-file-height="919" /></a></span></div></div></div><div class="trow"><div class="tsingle" style="width:190px;max-width:190px"><div class="thumbimage" style="height:98px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Fotothek_df_tg_0003625,_crop_rhombicosidodecahedron.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Fotothek_df_tg_0003625%2C_crop_rhombicosidodecahedron.jpg/188px-Fotothek_df_tg_0003625%2C_crop_rhombicosidodecahedron.jpg" decoding="async" width="188" height="98" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Fotothek_df_tg_0003625%2C_crop_rhombicosidodecahedron.jpg/282px-Fotothek_df_tg_0003625%2C_crop_rhombicosidodecahedron.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/Fotothek_df_tg_0003625%2C_crop_rhombicosidodecahedron.jpg/376px-Fotothek_df_tg_0003625%2C_crop_rhombicosidodecahedron.jpg 2x" data-file-width="573" data-file-height="299" /></a></span></div></div></div><div class="trow" style="display:flex"><div class="thumbcaption">Orthogonal projections in <i>Geometria</i> (1543) by <a href="/wiki/Augustin_Hirschvogel" title="Augustin Hirschvogel">Augustin Hirschvogel</a></div></div></div></div> <p>The <i>rhombicosidodecahedron</i> has six special <a href="/wiki/Orthogonal_projection" class="mw-redirect" title="Orthogonal projection">orthogonal projections</a>, centered, on a vertex, on two types of edges, and three types of faces: triangles, squares, and pentagons. The last two correspond to the A<sub>2</sub> and H<sub>2</sub> <a href="/wiki/Coxeter_plane" class="mw-redirect" title="Coxeter plane">Coxeter planes</a>. </p> <table class="wikitable" width="640"> <caption>Orthogonal projections </caption> <tbody><tr> <th>Centered by </th> <th>Vertex </th> <th>Edge<br />3-4 </th> <th>Edge<br />5-4 </th> <th>Face<br />Square </th> <th>Face<br />Triangle </th> <th>Face<br />Pentagon </th></tr> <tr> <th>Solid </th> <td> </td> <td> </td> <td> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_small_rhombi_12-20_from_blue_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Polyhedron_small_rhombi_12-20_from_blue_max.png/100px-Polyhedron_small_rhombi_12-20_from_blue_max.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Polyhedron_small_rhombi_12-20_from_blue_max.png/150px-Polyhedron_small_rhombi_12-20_from_blue_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Polyhedron_small_rhombi_12-20_from_blue_max.png/200px-Polyhedron_small_rhombi_12-20_from_blue_max.png 2x" data-file-width="1421" data-file-height="1424" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_small_rhombi_12-20_from_yellow_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Polyhedron_small_rhombi_12-20_from_yellow_max.png/100px-Polyhedron_small_rhombi_12-20_from_yellow_max.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Polyhedron_small_rhombi_12-20_from_yellow_max.png/150px-Polyhedron_small_rhombi_12-20_from_yellow_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/20/Polyhedron_small_rhombi_12-20_from_yellow_max.png/200px-Polyhedron_small_rhombi_12-20_from_yellow_max.png 2x" data-file-width="1453" data-file-height="1452" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_small_rhombi_12-20_from_red_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/12/Polyhedron_small_rhombi_12-20_from_red_max.png/100px-Polyhedron_small_rhombi_12-20_from_red_max.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/12/Polyhedron_small_rhombi_12-20_from_red_max.png/150px-Polyhedron_small_rhombi_12-20_from_red_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/12/Polyhedron_small_rhombi_12-20_from_red_max.png/200px-Polyhedron_small_rhombi_12-20_from_red_max.png 2x" data-file-width="1471" data-file-height="1471" /></a></span> </td></tr> <tr> <th>Wireframe </th> <td><span typeof="mw:File"><a href="/wiki/File:Dodecahedron_t02_v.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Dodecahedron_t02_v.png/100px-Dodecahedron_t02_v.png" decoding="async" width="100" height="102" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Dodecahedron_t02_v.png/150px-Dodecahedron_t02_v.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Dodecahedron_t02_v.png/200px-Dodecahedron_t02_v.png 2x" data-file-width="850" data-file-height="866" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dodecahedron_t02_e34.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Dodecahedron_t02_e34.png/100px-Dodecahedron_t02_e34.png" decoding="async" width="100" height="103" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Dodecahedron_t02_e34.png/150px-Dodecahedron_t02_e34.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Dodecahedron_t02_e34.png/200px-Dodecahedron_t02_e34.png 2x" data-file-width="849" data-file-height="872" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dodecahedron_t02_e45.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/12/Dodecahedron_t02_e45.png/100px-Dodecahedron_t02_e45.png" decoding="async" width="100" height="101" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/12/Dodecahedron_t02_e45.png/150px-Dodecahedron_t02_e45.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/12/Dodecahedron_t02_e45.png/200px-Dodecahedron_t02_e45.png 2x" data-file-width="857" data-file-height="865" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dodecahedron_t02_f4.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Dodecahedron_t02_f4.png/100px-Dodecahedron_t02_f4.png" decoding="async" width="100" height="98" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Dodecahedron_t02_f4.png/150px-Dodecahedron_t02_f4.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Dodecahedron_t02_f4.png/200px-Dodecahedron_t02_f4.png 2x" data-file-width="921" data-file-height="901" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dodecahedron_t02_A2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Dodecahedron_t02_A2.png/100px-Dodecahedron_t02_A2.png" decoding="async" width="100" height="98" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Dodecahedron_t02_A2.png/150px-Dodecahedron_t02_A2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/98/Dodecahedron_t02_A2.png/200px-Dodecahedron_t02_A2.png 2x" data-file-width="929" data-file-height="908" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dodecahedron_t02_H3.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Dodecahedron_t02_H3.png/100px-Dodecahedron_t02_H3.png" decoding="async" width="100" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Dodecahedron_t02_H3.png/150px-Dodecahedron_t02_H3.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Dodecahedron_t02_H3.png/200px-Dodecahedron_t02_H3.png 2x" data-file-width="830" data-file-height="867" /></a></span> </td></tr> <tr align="center"> <th>Projective<br />symmetry </th> <td>[2] </td> <td>[2] </td> <td>[2] </td> <td>[2] </td> <td>[6] </td> <td>[10] </td></tr> <tr> <th>Dual<br />image </th> <td><span typeof="mw:File"><a href="/wiki/File:Dual_dodecahedron_t02_v.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/18/Dual_dodecahedron_t02_v.png/100px-Dual_dodecahedron_t02_v.png" decoding="async" width="100" height="102" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/18/Dual_dodecahedron_t02_v.png/150px-Dual_dodecahedron_t02_v.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/18/Dual_dodecahedron_t02_v.png/200px-Dual_dodecahedron_t02_v.png 2x" data-file-width="546" data-file-height="559" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dual_dodecahedron_t02_e34.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Dual_dodecahedron_t02_e34.png/100px-Dual_dodecahedron_t02_e34.png" decoding="async" width="100" height="99" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Dual_dodecahedron_t02_e34.png/150px-Dual_dodecahedron_t02_e34.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Dual_dodecahedron_t02_e34.png/200px-Dual_dodecahedron_t02_e34.png 2x" data-file-width="598" data-file-height="590" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dual_dodecahedron_t02_e45.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Dual_dodecahedron_t02_e45.png/100px-Dual_dodecahedron_t02_e45.png" decoding="async" width="100" height="97" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Dual_dodecahedron_t02_e45.png/150px-Dual_dodecahedron_t02_e45.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/06/Dual_dodecahedron_t02_e45.png/200px-Dual_dodecahedron_t02_e45.png 2x" data-file-width="598" data-file-height="579" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dual_dodecahedron_t02_f4.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/Dual_dodecahedron_t02_f4.png/100px-Dual_dodecahedron_t02_f4.png" decoding="async" width="100" height="99" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/Dual_dodecahedron_t02_f4.png/150px-Dual_dodecahedron_t02_f4.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/57/Dual_dodecahedron_t02_f4.png/200px-Dual_dodecahedron_t02_f4.png 2x" data-file-width="594" data-file-height="589" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dual_dodecahedron_t02_A2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Dual_dodecahedron_t02_A2.png/100px-Dual_dodecahedron_t02_A2.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Dual_dodecahedron_t02_A2.png/150px-Dual_dodecahedron_t02_A2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Dual_dodecahedron_t02_A2.png/200px-Dual_dodecahedron_t02_A2.png 2x" data-file-width="592" data-file-height="592" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dual_dodecahedron_t02_H3.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Dual_dodecahedron_t02_H3.png/100px-Dual_dodecahedron_t02_H3.png" decoding="async" width="100" height="96" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Dual_dodecahedron_t02_H3.png/150px-Dual_dodecahedron_t02_H3.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Dual_dodecahedron_t02_H3.png/200px-Dual_dodecahedron_t02_H3.png 2x" data-file-width="595" data-file-height="574" /></a></span> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Spherical_tiling">Spherical tiling</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rhombicosidodecahedron&action=edit&section=6" title="Edit section: Spherical tiling"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The rhombicosidodecahedron can also be represented as a <a href="/wiki/Spherical_tiling" class="mw-redirect" title="Spherical tiling">spherical tiling</a>, and projected onto the plane via a <a href="/wiki/Stereographic_projection" title="Stereographic projection">stereographic projection</a>. This projection is <a href="/wiki/Conformal_map" title="Conformal map">conformal</a>, preserving angles but not areas or lengths. Straight lines on the sphere are projected as circular arcs on the plane. </p> <table class="wikitable"> <tbody><tr align="center" valign="top"> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_tiling_532-t02.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Uniform_tiling_532-t02.png/160px-Uniform_tiling_532-t02.png" decoding="async" width="160" height="160" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Uniform_tiling_532-t02.png/240px-Uniform_tiling_532-t02.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Uniform_tiling_532-t02.png/320px-Uniform_tiling_532-t02.png 2x" data-file-width="829" data-file-height="828" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Rhombicosidodecahedron_stereographic_projection_pentagon%27.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Rhombicosidodecahedron_stereographic_projection_pentagon%27.png/160px-Rhombicosidodecahedron_stereographic_projection_pentagon%27.png" decoding="async" width="160" height="163" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Rhombicosidodecahedron_stereographic_projection_pentagon%27.png/240px-Rhombicosidodecahedron_stereographic_projection_pentagon%27.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Rhombicosidodecahedron_stereographic_projection_pentagon%27.png/320px-Rhombicosidodecahedron_stereographic_projection_pentagon%27.png 2x" data-file-width="883" data-file-height="900" /></a></span><br /><a href="/wiki/Pentagon" title="Pentagon">Pentagon</a>-centered </td> <td><span typeof="mw:File"><a href="/wiki/File:Rhombicosidodecahedron_stereographic_projection_triangle.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Rhombicosidodecahedron_stereographic_projection_triangle.png/160px-Rhombicosidodecahedron_stereographic_projection_triangle.png" decoding="async" width="160" height="154" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Rhombicosidodecahedron_stereographic_projection_triangle.png/240px-Rhombicosidodecahedron_stereographic_projection_triangle.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/60/Rhombicosidodecahedron_stereographic_projection_triangle.png/320px-Rhombicosidodecahedron_stereographic_projection_triangle.png 2x" data-file-width="893" data-file-height="861" /></a></span><br /><a href="/wiki/Triangle" title="Triangle">Triangle</a>-centered </td> <td><span typeof="mw:File"><a href="/wiki/File:Rhombicosidodecahedron_stereographic_projection_square.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/29/Rhombicosidodecahedron_stereographic_projection_square.png/160px-Rhombicosidodecahedron_stereographic_projection_square.png" decoding="async" width="160" height="157" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/29/Rhombicosidodecahedron_stereographic_projection_square.png/240px-Rhombicosidodecahedron_stereographic_projection_square.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/29/Rhombicosidodecahedron_stereographic_projection_square.png/320px-Rhombicosidodecahedron_stereographic_projection_square.png 2x" data-file-width="916" data-file-height="899" /></a></span><br /><a href="/wiki/Square" title="Square">Square</a>-centered </td></tr> <tr> <th><a href="/wiki/Orthographic_projection" title="Orthographic projection">Orthographic projection</a> </th> <th colspan="3"><a href="/wiki/Stereographic_projection" title="Stereographic projection">Stereographic projections</a> </th></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Related_polyhedra">Related polyhedra</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rhombicosidodecahedron&action=edit&section=7" title="Edit section: Related polyhedra"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:P4-A11-P5.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/5a/P4-A11-P5.gif" decoding="async" width="160" height="160" class="mw-file-element" data-file-width="160" data-file-height="160" /></a><figcaption><a href="/wiki/Expansion_(geometry)" title="Expansion (geometry)">Expansion</a> of either a <a href="/wiki/Dodecahedron" title="Dodecahedron">dodecahedron</a> or an <a href="/wiki/Icosahedron" title="Icosahedron">icosahedron</a> creates a rhombicosidodecahedron.</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Zome_vertices.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Zome_vertices.jpg/160px-Zome_vertices.jpg" decoding="async" width="160" height="231" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Zome_vertices.jpg/240px-Zome_vertices.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Zome_vertices.jpg/320px-Zome_vertices.jpg 2x" data-file-width="353" data-file-height="509" /></a><figcaption>A version with golden rectangles is used as vertex element of the <a href="/wiki/Construction_set" title="Construction set">construction set</a> <a href="/wiki/Zometool" title="Zometool">Zometool</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></figcaption></figure> <table class="wikitable mw-collapsible mw-collapsed"> <tbody><tr> <th colspan="8">Family of uniform icosahedral polyhedra </th></tr> <tr style="text-align:center;"> <th colspan="7"><a href="/wiki/List_of_spherical_symmetry_groups" title="List of spherical symmetry groups">Symmetry</a>: <a href="/wiki/Icosahedral_symmetry" title="Icosahedral symmetry">[5,3]</a>, (*532) </th> <th>[5,3]<sup>+</sup>, (532) </th></tr> <tr style="text-align:center;"> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_polyhedron-53-t0.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Uniform_polyhedron-53-t0.svg/50px-Uniform_polyhedron-53-t0.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Uniform_polyhedron-53-t0.svg/75px-Uniform_polyhedron-53-t0.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Uniform_polyhedron-53-t0.svg/100px-Uniform_polyhedron-53-t0.svg.png 2x" data-file-width="800" data-file-height="800" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_polyhedron-53-t01.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/Uniform_polyhedron-53-t01.svg/50px-Uniform_polyhedron-53-t01.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/Uniform_polyhedron-53-t01.svg/75px-Uniform_polyhedron-53-t01.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/34/Uniform_polyhedron-53-t01.svg/100px-Uniform_polyhedron-53-t01.svg.png 2x" data-file-width="750" data-file-height="750" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_polyhedron-53-t1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Uniform_polyhedron-53-t1.svg/50px-Uniform_polyhedron-53-t1.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Uniform_polyhedron-53-t1.svg/75px-Uniform_polyhedron-53-t1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Uniform_polyhedron-53-t1.svg/100px-Uniform_polyhedron-53-t1.svg.png 2x" data-file-width="800" data-file-height="800" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_polyhedron-53-t12.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Uniform_polyhedron-53-t12.svg/50px-Uniform_polyhedron-53-t12.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Uniform_polyhedron-53-t12.svg/75px-Uniform_polyhedron-53-t12.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Uniform_polyhedron-53-t12.svg/100px-Uniform_polyhedron-53-t12.svg.png 2x" data-file-width="800" data-file-height="800" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_polyhedron-53-t2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Uniform_polyhedron-53-t2.svg/50px-Uniform_polyhedron-53-t2.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Uniform_polyhedron-53-t2.svg/75px-Uniform_polyhedron-53-t2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Uniform_polyhedron-53-t2.svg/100px-Uniform_polyhedron-53-t2.svg.png 2x" data-file-width="800" data-file-height="800" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_polyhedron-53-t02.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Uniform_polyhedron-53-t02.png/50px-Uniform_polyhedron-53-t02.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Uniform_polyhedron-53-t02.png/75px-Uniform_polyhedron-53-t02.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Uniform_polyhedron-53-t02.png/100px-Uniform_polyhedron-53-t02.png 2x" data-file-width="779" data-file-height="780" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_polyhedron-53-t012.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Uniform_polyhedron-53-t012.png/50px-Uniform_polyhedron-53-t012.png" decoding="async" width="50" height="51" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Uniform_polyhedron-53-t012.png/75px-Uniform_polyhedron-53-t012.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Uniform_polyhedron-53-t012.png/100px-Uniform_polyhedron-53-t012.png 2x" data-file-width="776" data-file-height="789" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_polyhedron-53-s012.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Uniform_polyhedron-53-s012.png/50px-Uniform_polyhedron-53-s012.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Uniform_polyhedron-53-s012.png/75px-Uniform_polyhedron-53-s012.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/52/Uniform_polyhedron-53-s012.png/100px-Uniform_polyhedron-53-s012.png 2x" data-file-width="1000" data-file-height="1000" /></a></span> </td></tr> <tr style="text-align:center;"> <th><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.png" decoding="async" width="7" height="23" class="mw-file-element" data-file-width="7" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span></span> </th> <th><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.png" decoding="async" width="7" height="23" class="mw-file-element" data-file-width="7" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span></span> </th> <th><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.png" decoding="async" width="7" height="23" class="mw-file-element" data-file-width="7" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span></span> </th> <th><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.png" decoding="async" width="7" height="23" class="mw-file-element" data-file-width="7" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span></span> </th> <th><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.png" decoding="async" width="7" height="23" class="mw-file-element" data-file-width="7" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span></span> </th> <th><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.png" decoding="async" width="7" height="23" class="mw-file-element" data-file-width="7" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span></span> </th> <th><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.png" decoding="async" width="7" height="23" class="mw-file-element" data-file-width="7" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span></span> </th> <th><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/2/28/CDel_node_h.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_5.png" decoding="async" width="7" height="23" class="mw-file-element" data-file-width="7" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/2/28/CDel_node_h.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/2/28/CDel_node_h.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span></span> </th></tr> <tr style="text-align:center;"> <td><a href="/wiki/Dodecahedron" title="Dodecahedron">{5,3}</a> </td> <td><a href="/wiki/Truncated_dodecahedron" title="Truncated dodecahedron">t{5,3}</a> </td> <td><a href="/wiki/Icosidodecahedron" title="Icosidodecahedron">r{5,3}</a> </td> <td><a href="/wiki/Truncated_icosahedron" title="Truncated icosahedron">t{3,5}</a> </td> <td><a href="/wiki/Icosahedron" title="Icosahedron">{3,5}</a> </td> <td><a class="mw-selflink selflink">rr{5,3}</a> </td> <td><a href="/wiki/Truncated_icosidodecahedron" title="Truncated icosidodecahedron">tr{5,3}</a> </td> <td><a href="/wiki/Snub_dodecahedron" title="Snub dodecahedron">sr{5,3}</a> </td></tr> <tr style="text-align:center;"> <th colspan="8">Duals to uniform polyhedra </th></tr> <tr style="text-align:center;"> <td><span typeof="mw:File"><a href="/wiki/File:Icosahedron.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Icosahedron.svg/50px-Icosahedron.svg.png" decoding="async" width="50" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Icosahedron.svg/75px-Icosahedron.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Icosahedron.svg/100px-Icosahedron.svg.png 2x" data-file-width="512" data-file-height="492" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Triakisicosahedron.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Triakisicosahedron.jpg/50px-Triakisicosahedron.jpg" decoding="async" width="50" height="52" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Triakisicosahedron.jpg/75px-Triakisicosahedron.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Triakisicosahedron.jpg/100px-Triakisicosahedron.jpg 2x" data-file-width="819" data-file-height="849" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Rhombictriacontahedron.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Rhombictriacontahedron.svg/50px-Rhombictriacontahedron.svg.png" decoding="async" width="50" height="55" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Rhombictriacontahedron.svg/75px-Rhombictriacontahedron.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Rhombictriacontahedron.svg/100px-Rhombictriacontahedron.svg.png 2x" data-file-width="560" data-file-height="620" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Pentakisdodecahedron.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Pentakisdodecahedron.jpg/50px-Pentakisdodecahedron.jpg" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Pentakisdodecahedron.jpg/75px-Pentakisdodecahedron.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Pentakisdodecahedron.jpg/100px-Pentakisdodecahedron.jpg 2x" data-file-width="844" data-file-height="843" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dodecahedron.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Dodecahedron.svg/50px-Dodecahedron.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Dodecahedron.svg/75px-Dodecahedron.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Dodecahedron.svg/100px-Dodecahedron.svg.png 2x" data-file-width="300" data-file-height="300" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Deltoidalhexecontahedron.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Deltoidalhexecontahedron.jpg/50px-Deltoidalhexecontahedron.jpg" decoding="async" width="50" height="49" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Deltoidalhexecontahedron.jpg/75px-Deltoidalhexecontahedron.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Deltoidalhexecontahedron.jpg/100px-Deltoidalhexecontahedron.jpg 2x" data-file-width="854" data-file-height="843" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Disdyakistriacontahedron.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Disdyakistriacontahedron.jpg/50px-Disdyakistriacontahedron.jpg" decoding="async" width="50" height="52" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Disdyakistriacontahedron.jpg/75px-Disdyakistriacontahedron.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Disdyakistriacontahedron.jpg/100px-Disdyakistriacontahedron.jpg 2x" data-file-width="812" data-file-height="847" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Pentagonalhexecontahedronccw.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Pentagonalhexecontahedronccw.jpg/50px-Pentagonalhexecontahedronccw.jpg" decoding="async" width="50" height="51" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Pentagonalhexecontahedronccw.jpg/75px-Pentagonalhexecontahedronccw.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/90/Pentagonalhexecontahedronccw.jpg/100px-Pentagonalhexecontahedronccw.jpg 2x" data-file-width="834" data-file-height="851" /></a></span> </td></tr> <tr style="text-align:center;"> <td><a href="/wiki/Icosahedron" title="Icosahedron">V5.5.5</a> </td> <td><a href="/wiki/Triakis_icosahedron" title="Triakis icosahedron">V3.10.10</a> </td> <td><a href="/wiki/Rhombic_triacontahedron" title="Rhombic triacontahedron">V3.5.3.5</a> </td> <td><a href="/wiki/Pentakis_dodecahedron" title="Pentakis dodecahedron">V5.6.6</a> </td> <td><a href="/wiki/Dodecahedron" title="Dodecahedron">V3.3.3.3.3</a> </td> <td><a href="/wiki/Deltoidal_hexecontahedron" title="Deltoidal hexecontahedron">V3.4.5.4</a> </td> <td><a href="/wiki/Disdyakis_triacontahedron" title="Disdyakis triacontahedron">V4.6.10</a> </td> <td><a href="/wiki/Pentagonal_hexecontahedron" title="Pentagonal hexecontahedron">V3.3.3.3.5</a> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Symmetry_mutations">Symmetry mutations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rhombicosidodecahedron&action=edit&section=8" title="Edit section: Symmetry mutations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>This polyhedron is topologically related as a part of a sequence of <a href="/wiki/Cantellation_(geometry)" title="Cantellation (geometry)">cantellated</a> polyhedra with vertex figure (3.4.n.4), which continues as tilings of the <a href="/wiki/Hyperbolic_space" title="Hyperbolic space">hyperbolic plane</a>. These <a href="/wiki/Vertex-transitive" class="mw-redirect" title="Vertex-transitive">vertex-transitive</a> figures have (*n32) reflectional <a href="/wiki/Orbifold_notation" title="Orbifold notation">symmetry</a>. </p> <table class="wikitable mw-collapsible mw-collapsed"> <tbody><tr> <th colspan="9">*<i>n</i>32 symmetry mutation of expanded tilings: 3.4.<i>n</i>.4 </th></tr> <tr> <th rowspan="2">Symmetry<br />*<i>n</i>32<br />[n,3] </th> <th colspan="4"><a href="/wiki/List_of_spherical_symmetry_groups" title="List of spherical symmetry groups">Spherical</a> </th> <th><a href="/wiki/List_of_planar_symmetry_groups" title="List of planar symmetry groups">Euclid.</a> </th> <th colspan="2">Compact hyperb. </th> <th>Paracomp. </th></tr> <tr style="text-align:center;"> <th>*232<br />[2,3] </th> <th>*332<br />[3,3] </th> <th>*432<br />[4,3] </th> <th>*532<br />[5,3] </th> <th>*632<br />[6,3] </th> <th>*732<br />[7,3] </th> <th>*832<br />[8,3]... </th> <th>*∞32<br />[∞,3] </th></tr> <tr style="text-align:center;"> <th>Figure </th> <td><span typeof="mw:File"><a href="/wiki/File:Spherical_triangular_prism.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Spherical_triangular_prism.svg/50px-Spherical_triangular_prism.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Spherical_triangular_prism.svg/75px-Spherical_triangular_prism.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Spherical_triangular_prism.svg/100px-Spherical_triangular_prism.svg.png 2x" data-file-width="577" data-file-height="577" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_tiling_332-t02.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Uniform_tiling_332-t02.png/50px-Uniform_tiling_332-t02.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Uniform_tiling_332-t02.png/75px-Uniform_tiling_332-t02.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Uniform_tiling_332-t02.png/100px-Uniform_tiling_332-t02.png 2x" data-file-width="816" data-file-height="813" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_tiling_432-t02.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Uniform_tiling_432-t02.png/50px-Uniform_tiling_432-t02.png" decoding="async" width="50" height="51" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Uniform_tiling_432-t02.png/75px-Uniform_tiling_432-t02.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Uniform_tiling_432-t02.png/100px-Uniform_tiling_432-t02.png 2x" data-file-width="828" data-file-height="838" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_tiling_532-t02.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Uniform_tiling_532-t02.png/50px-Uniform_tiling_532-t02.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Uniform_tiling_532-t02.png/75px-Uniform_tiling_532-t02.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Uniform_tiling_532-t02.png/100px-Uniform_tiling_532-t02.png 2x" data-file-width="829" data-file-height="828" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Uniform_polyhedron-63-t02.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Uniform_polyhedron-63-t02.png/50px-Uniform_polyhedron-63-t02.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Uniform_polyhedron-63-t02.png/75px-Uniform_polyhedron-63-t02.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Uniform_polyhedron-63-t02.png/100px-Uniform_polyhedron-63-t02.png 2x" data-file-width="802" data-file-height="802" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Rhombitriheptagonal_tiling.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Rhombitriheptagonal_tiling.svg/50px-Rhombitriheptagonal_tiling.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Rhombitriheptagonal_tiling.svg/75px-Rhombitriheptagonal_tiling.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Rhombitriheptagonal_tiling.svg/100px-Rhombitriheptagonal_tiling.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:H2-8-3-cantellated.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/H2-8-3-cantellated.svg/50px-H2-8-3-cantellated.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/H2-8-3-cantellated.svg/75px-H2-8-3-cantellated.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e8/H2-8-3-cantellated.svg/100px-H2-8-3-cantellated.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:H2_tiling_23i-5.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/H2_tiling_23i-5.png/50px-H2_tiling_23i-5.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/H2_tiling_23i-5.png/75px-H2_tiling_23i-5.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0f/H2_tiling_23i-5.png/100px-H2_tiling_23i-5.png 2x" data-file-width="2520" data-file-height="2520" /></a></span> </td></tr> <tr> <th><a href="/wiki/Vertex_configuration" title="Vertex configuration">Config.</a> </th> <th><a href="/wiki/Triangular_prism" title="Triangular prism">3.4.2.4</a> </th> <th><a href="/wiki/Cuboctahedron" title="Cuboctahedron">3.4.3.4</a> </th> <th><a href="/wiki/Rhombicuboctahedron" title="Rhombicuboctahedron">3.4.4.4</a> </th> <th><a class="mw-selflink selflink">3.4.5.4</a> </th> <th><a href="/wiki/Rhombitrihexagonal_tiling" title="Rhombitrihexagonal tiling">3.4.6.4</a> </th> <th><a href="/wiki/Rhombitriheptagonal_tiling" title="Rhombitriheptagonal tiling">3.4.7.4</a> </th> <th><a href="/wiki/Rhombitrioctagonal_tiling" title="Rhombitrioctagonal tiling">3.4.8.4</a> </th> <th><a href="/wiki/Rhombitriapeirogonal_tiling" title="Rhombitriapeirogonal tiling">3.4.∞.4</a> </th></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Johnson_solids">Johnson solids</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rhombicosidodecahedron&action=edit&section=9" title="Edit section: Johnson solids"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There are 12 related <a href="/wiki/Johnson_solid" title="Johnson solid">Johnson solids</a>, 5 by diminishment, and 8 including gyrations: </p> <table class="wikitable"> <caption>Diminished </caption> <tbody><tr align="center"> <td><a href="/wiki/Pentagonal_cupola" title="Pentagonal cupola">J5</a><br /><span typeof="mw:File"><a href="/wiki/File:Pentagonal_cupola.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Pentagonal_cupola.png/100px-Pentagonal_cupola.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Pentagonal_cupola.png/150px-Pentagonal_cupola.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Pentagonal_cupola.png/200px-Pentagonal_cupola.png 2x" data-file-width="420" data-file-height="419" /></a></span> </td> <td><a href="/wiki/Diminished_rhombicosidodecahedron" title="Diminished rhombicosidodecahedron">76</a><br /><span typeof="mw:File"><a href="/wiki/File:Diminished_rhombicosidodecahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Diminished_rhombicosidodecahedron.png/100px-Diminished_rhombicosidodecahedron.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Diminished_rhombicosidodecahedron.png/150px-Diminished_rhombicosidodecahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/69/Diminished_rhombicosidodecahedron.png/200px-Diminished_rhombicosidodecahedron.png 2x" data-file-width="512" data-file-height="512" /></a></span> </td> <td><a href="/wiki/Parabidiminished_rhombicosidodecahedron" title="Parabidiminished rhombicosidodecahedron">80</a><br /><span typeof="mw:File"><a href="/wiki/File:Parabidiminished_rhombicosidodecahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Parabidiminished_rhombicosidodecahedron.png/100px-Parabidiminished_rhombicosidodecahedron.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Parabidiminished_rhombicosidodecahedron.png/150px-Parabidiminished_rhombicosidodecahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Parabidiminished_rhombicosidodecahedron.png/200px-Parabidiminished_rhombicosidodecahedron.png 2x" data-file-width="512" data-file-height="512" /></a></span> </td> <td><a href="/wiki/Metabidiminished_rhombicosidodecahedron" title="Metabidiminished rhombicosidodecahedron">81</a><br /><span typeof="mw:File"><a href="/wiki/File:Metabidiminished_rhombicosidodecahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Metabidiminished_rhombicosidodecahedron.png/100px-Metabidiminished_rhombicosidodecahedron.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Metabidiminished_rhombicosidodecahedron.png/150px-Metabidiminished_rhombicosidodecahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/40/Metabidiminished_rhombicosidodecahedron.png/200px-Metabidiminished_rhombicosidodecahedron.png 2x" data-file-width="512" data-file-height="512" /></a></span> </td> <td><a href="/wiki/Tridiminished_rhombicosidodecahedron" title="Tridiminished rhombicosidodecahedron">83</a><br /><span typeof="mw:File"><a href="/wiki/File:Tridiminished_rhombicosidodecahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Tridiminished_rhombicosidodecahedron.png/100px-Tridiminished_rhombicosidodecahedron.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Tridiminished_rhombicosidodecahedron.png/150px-Tridiminished_rhombicosidodecahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/Tridiminished_rhombicosidodecahedron.png/200px-Tridiminished_rhombicosidodecahedron.png 2x" data-file-width="512" data-file-height="512" /></a></span> </td></tr></tbody></table> <table class="wikitable"> <caption>Gyrated and/or diminished </caption> <tbody><tr align="center"> <td><a href="/wiki/Gyrate_rhombicosidodecahedron" title="Gyrate rhombicosidodecahedron">72</a><br /><span typeof="mw:File"><a href="/wiki/File:Gyrate_rhombicosidodecahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Gyrate_rhombicosidodecahedron.png/100px-Gyrate_rhombicosidodecahedron.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Gyrate_rhombicosidodecahedron.png/150px-Gyrate_rhombicosidodecahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/db/Gyrate_rhombicosidodecahedron.png/200px-Gyrate_rhombicosidodecahedron.png 2x" data-file-width="512" data-file-height="512" /></a></span> </td> <td><a href="/wiki/Parabigyrate_rhombicosidodecahedron" title="Parabigyrate rhombicosidodecahedron">73</a><br /><span typeof="mw:File"><a href="/wiki/File:Parabigyrate_rhombicosidodecahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/48/Parabigyrate_rhombicosidodecahedron.png/100px-Parabigyrate_rhombicosidodecahedron.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/48/Parabigyrate_rhombicosidodecahedron.png/150px-Parabigyrate_rhombicosidodecahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/48/Parabigyrate_rhombicosidodecahedron.png/200px-Parabigyrate_rhombicosidodecahedron.png 2x" data-file-width="512" data-file-height="512" /></a></span> </td> <td><a href="/wiki/Metabigyrate_rhombicosidodecahedron" title="Metabigyrate rhombicosidodecahedron">74</a><br /><span typeof="mw:File"><a href="/wiki/File:Metabigyrate_rhombicosidodecahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Metabigyrate_rhombicosidodecahedron.png/100px-Metabigyrate_rhombicosidodecahedron.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Metabigyrate_rhombicosidodecahedron.png/150px-Metabigyrate_rhombicosidodecahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/44/Metabigyrate_rhombicosidodecahedron.png/200px-Metabigyrate_rhombicosidodecahedron.png 2x" data-file-width="512" data-file-height="512" /></a></span> </td> <td><a href="/wiki/Trigyrate_rhombicosidodecahedron" title="Trigyrate rhombicosidodecahedron">75</a><br /><span typeof="mw:File"><a href="/wiki/File:Trigyrate_rhombicosidodecahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/Trigyrate_rhombicosidodecahedron.png/100px-Trigyrate_rhombicosidodecahedron.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/Trigyrate_rhombicosidodecahedron.png/150px-Trigyrate_rhombicosidodecahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/71/Trigyrate_rhombicosidodecahedron.png/200px-Trigyrate_rhombicosidodecahedron.png 2x" data-file-width="512" data-file-height="512" /></a></span> </td></tr> <tr align="center"> <td><a href="/wiki/Paragyrate_diminished_rhombicosidodecahedron" title="Paragyrate diminished rhombicosidodecahedron">77</a><br /><span typeof="mw:File"><a href="/wiki/File:Paragyrate_diminished_rhombicosidodecahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Paragyrate_diminished_rhombicosidodecahedron.png/100px-Paragyrate_diminished_rhombicosidodecahedron.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Paragyrate_diminished_rhombicosidodecahedron.png/150px-Paragyrate_diminished_rhombicosidodecahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/66/Paragyrate_diminished_rhombicosidodecahedron.png/200px-Paragyrate_diminished_rhombicosidodecahedron.png 2x" data-file-width="512" data-file-height="512" /></a></span> </td> <td><a href="/wiki/Metagyrate_diminished_rhombicosidodecahedron" title="Metagyrate diminished rhombicosidodecahedron">78</a><br /><span typeof="mw:File"><a href="/wiki/File:Metagyrate_diminished_rhombicosidodecahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Metagyrate_diminished_rhombicosidodecahedron.png/100px-Metagyrate_diminished_rhombicosidodecahedron.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Metagyrate_diminished_rhombicosidodecahedron.png/150px-Metagyrate_diminished_rhombicosidodecahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Metagyrate_diminished_rhombicosidodecahedron.png/200px-Metagyrate_diminished_rhombicosidodecahedron.png 2x" data-file-width="512" data-file-height="512" /></a></span> </td> <td><a href="/wiki/Bigyrate_diminished_rhombicosidodecahedron" title="Bigyrate diminished rhombicosidodecahedron">79</a><br /><span typeof="mw:File"><a href="/wiki/File:Bigyrate_diminished_rhombicosidodecahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Bigyrate_diminished_rhombicosidodecahedron.png/100px-Bigyrate_diminished_rhombicosidodecahedron.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Bigyrate_diminished_rhombicosidodecahedron.png/150px-Bigyrate_diminished_rhombicosidodecahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/97/Bigyrate_diminished_rhombicosidodecahedron.png/200px-Bigyrate_diminished_rhombicosidodecahedron.png 2x" data-file-width="512" data-file-height="512" /></a></span> </td> <td><a href="/wiki/Gyrate_bidiminished_rhombicosidodecahedron" title="Gyrate bidiminished rhombicosidodecahedron">82</a><br /><span typeof="mw:File"><a href="/wiki/File:Gyrate_bidiminished_rhombicosidodecahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Gyrate_bidiminished_rhombicosidodecahedron.png/100px-Gyrate_bidiminished_rhombicosidodecahedron.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Gyrate_bidiminished_rhombicosidodecahedron.png/150px-Gyrate_bidiminished_rhombicosidodecahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/54/Gyrate_bidiminished_rhombicosidodecahedron.png/200px-Gyrate_bidiminished_rhombicosidodecahedron.png 2x" data-file-width="512" data-file-height="512" /></a></span> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Vertex_arrangement">Vertex arrangement</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rhombicosidodecahedron&action=edit&section=10" title="Edit section: Vertex arrangement"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The rhombicosidodecahedron shares its <a href="/wiki/Vertex_arrangement" title="Vertex arrangement">vertex arrangement</a> with three <a href="/wiki/Nonconvex_uniform_polyhedra" class="mw-redirect" title="Nonconvex uniform polyhedra">nonconvex uniform polyhedra</a>: the <a href="/wiki/Small_stellated_truncated_dodecahedron" title="Small stellated truncated dodecahedron">small stellated truncated dodecahedron</a>, the <a href="/wiki/Small_dodecicosidodecahedron" title="Small dodecicosidodecahedron">small dodecicosidodecahedron</a> (having the triangular and pentagonal faces in common), and the <a href="/wiki/Small_rhombidodecahedron" title="Small rhombidodecahedron">small rhombidodecahedron</a> (having the square faces in common). </p><p>It also shares its vertex arrangement with the <a href="/wiki/Polyhedron_compound#Uniform_compounds" class="mw-redirect" title="Polyhedron compound">uniform compounds</a> of <a href="/wiki/Compound_of_six_pentagrammic_prisms" title="Compound of six pentagrammic prisms">six</a> or <a href="/wiki/Compound_of_twelve_pentagrammic_prisms" title="Compound of twelve pentagrammic prisms">twelve pentagrammic prisms</a>. </p> <table class="wikitable" style="width:400px; vertical-align:top; text-align:center;"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/File:Small_rhombicosidodecahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Small_rhombicosidodecahedron.png/100px-Small_rhombicosidodecahedron.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Small_rhombicosidodecahedron.png/150px-Small_rhombicosidodecahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/31/Small_rhombicosidodecahedron.png/200px-Small_rhombicosidodecahedron.png 2x" data-file-width="1000" data-file-height="1000" /></a></span><br /><b>Rhombicosidodecahedron</b> </td> <td><span typeof="mw:File"><a href="/wiki/File:Small_dodecicosidodecahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/Small_dodecicosidodecahedron.png/100px-Small_dodecicosidodecahedron.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/Small_dodecicosidodecahedron.png/150px-Small_dodecicosidodecahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/61/Small_dodecicosidodecahedron.png/200px-Small_dodecicosidodecahedron.png 2x" data-file-width="1000" data-file-height="1000" /></a></span><br /><a href="/wiki/Small_dodecicosidodecahedron" title="Small dodecicosidodecahedron">Small dodecicosidodecahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Small_rhombidodecahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Small_rhombidodecahedron.png/100px-Small_rhombidodecahedron.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Small_rhombidodecahedron.png/150px-Small_rhombidodecahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Small_rhombidodecahedron.png/200px-Small_rhombidodecahedron.png 2x" data-file-width="1000" data-file-height="1000" /></a></span><br /><a href="/wiki/Small_rhombidodecahedron" title="Small rhombidodecahedron">Small rhombidodecahedron</a> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Small_stellated_truncated_dodecahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Small_stellated_truncated_dodecahedron.png/100px-Small_stellated_truncated_dodecahedron.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Small_stellated_truncated_dodecahedron.png/150px-Small_stellated_truncated_dodecahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Small_stellated_truncated_dodecahedron.png/200px-Small_stellated_truncated_dodecahedron.png 2x" data-file-width="1000" data-file-height="1000" /></a></span><br /><a href="/wiki/Small_stellated_truncated_dodecahedron" title="Small stellated truncated dodecahedron">Small stellated truncated dodecahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:UC36-6_pentagrammic_prisms.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/UC36-6_pentagrammic_prisms.png/100px-UC36-6_pentagrammic_prisms.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/UC36-6_pentagrammic_prisms.png/150px-UC36-6_pentagrammic_prisms.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/UC36-6_pentagrammic_prisms.png/200px-UC36-6_pentagrammic_prisms.png 2x" data-file-width="800" data-file-height="800" /></a></span><br /><a href="/wiki/Compound_of_six_pentagrammic_prisms" title="Compound of six pentagrammic prisms">Compound of six pentagrammic prisms</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:UC37-12_pentagrammic_prisms.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/UC37-12_pentagrammic_prisms.png/100px-UC37-12_pentagrammic_prisms.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/UC37-12_pentagrammic_prisms.png/150px-UC37-12_pentagrammic_prisms.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/UC37-12_pentagrammic_prisms.png/200px-UC37-12_pentagrammic_prisms.png 2x" data-file-width="800" data-file-height="800" /></a></span><br /><a href="/wiki/Compound_of_twelve_pentagrammic_prisms" title="Compound of twelve pentagrammic prisms">Compound of twelve pentagrammic prisms</a> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Rhombicosidodecahedral_graph">Rhombicosidodecahedral graph</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rhombicosidodecahedron&action=edit&section=11" title="Edit section: Rhombicosidodecahedral graph"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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">Rhombicosidodecahedral graph</th></tr><tr><td colspan="2" class="infobox-image"><span typeof="mw:File"><a href="/wiki/File:Rhombicosidodecahedral_graph.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Rhombicosidodecahedral_graph.png/240px-Rhombicosidodecahedral_graph.png" decoding="async" width="240" height="232" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Rhombicosidodecahedral_graph.png/360px-Rhombicosidodecahedral_graph.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Rhombicosidodecahedral_graph.png/480px-Rhombicosidodecahedral_graph.png 2x" data-file-width="1620" data-file-height="1568" /></a></span><div class="infobox-caption">Pentagon centered Schlegel diagram</div></td></tr><tr><th scope="row" class="infobox-label" style="width:50%;"><a href="/wiki/Vertex_(graph_theory)" title="Vertex (graph theory)">Vertices</a></th><td class="infobox-data">60</td></tr><tr><th scope="row" class="infobox-label" style="width:50%;"><a href="/wiki/Edge_(graph_theory)" class="mw-redirect" title="Edge (graph theory)">Edges</a></th><td class="infobox-data">120</td></tr><tr><th scope="row" class="infobox-label" style="width:50%;"><a href="/wiki/Graph_automorphism" title="Graph automorphism">Automorphisms</a></th><td class="infobox-data">120</td></tr><tr><th scope="row" class="infobox-label" style="width:50%;">Properties</th><td class="infobox-data"><a href="/wiki/Quartic_graph" title="Quartic graph">Quartic graph</a>, <a href="/wiki/Hamiltonian_graph" class="mw-redirect" title="Hamiltonian graph">Hamiltonian</a>, <a href="/wiki/Regular_graph" title="Regular graph">regular</a></td></tr><tr><td colspan="2" class="infobox-below"><a href="/wiki/List_of_graphs_by_edges_and_vertices" title="List of graphs by edges and vertices">Table of graphs and parameters</a></td></tr></tbody></table> <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>rhombicosidodecahedral graph</b> is the <a href="/wiki/1-skeleton" class="mw-redirect" title="1-skeleton">graph of vertices and edges</a> of the rhombicosidodecahedron, one of the <a href="/wiki/Archimedean_solid" title="Archimedean solid">Archimedean solids</a>. It has 60 <a href="/wiki/Vertex_(graph_theory)" title="Vertex (graph theory)">vertices</a> and 120 edges, and is a <a href="/wiki/Quartic_graph" title="Quartic graph">quartic graph</a> <a href="/wiki/Archimedean_graph" title="Archimedean graph">Archimedean graph</a>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Rhombicosidodecahedral_graph-squarecenter.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Rhombicosidodecahedral_graph-squarecenter.png/220px-Rhombicosidodecahedral_graph-squarecenter.png" decoding="async" width="220" height="190" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Rhombicosidodecahedral_graph-squarecenter.png/330px-Rhombicosidodecahedral_graph-squarecenter.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/50/Rhombicosidodecahedral_graph-squarecenter.png/440px-Rhombicosidodecahedral_graph-squarecenter.png 2x" data-file-width="1223" data-file-height="1055" /></a><figcaption>Square centered <a href="/wiki/Schlegel_diagram" title="Schlegel diagram">Schlegel diagram</a></figcaption></figure> <div style="clear:both;" class=""></div> <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=Rhombicosidodecahedron&action=edit&section=12" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Truncated_rhombicosidodecahedron" title="Truncated rhombicosidodecahedron">Truncated rhombicosidodecahedron</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rhombicosidodecahedron&action=edit&section=13" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><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="CITEREFIoannis_Keppler_[i.e.,_Johannes_Kepler]1619" class="citation book cs1">Ioannis Keppler [<i>i.e.</i>, <a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Johannes Kepler</a>] (1619). <a rel="nofollow" class="external text" href="https://archive.org/details/ioanniskepplerih00kepl/page/n87/mode/1up">"Liber II. De Congruentia Figurarum Harmonicarum. XXVIII. Propositio."</a> [Book II. On the Congruence of Harmonic Figures. Proposition XXVIII.]. <i><a href="/wiki/Harmonices_Mundi" title="Harmonices Mundi">Harmonices Mundi Libri V</a></i> [<i>The Harmony of the World in Five Books</i>]. Linz, Austria: Sumptibus Godofredi Tampachii bibl. Francof. excudebat Ioannes Plancus [published by Gottfried Tambach [...] printed by Johann Planck]. p. 64. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/863358134">863358134</a>. <q>Unus igitur Trigonicus cum duobus Tetragonicis & uno Pentagonico, minus efficiunt 4 rectis, & congruunt 20 Trigonicum 30 Tetragonis & 12 Pentagonis, in unum Hexacontadyhedron, quod appello Rhombicoſidodecaëdron, ſeu ſectum Rhombum Icoſidododecaëdricum.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Liber+II.+De+Congruentia+Figurarum+Harmonicarum.+XXVIII.+Propositio.&rft.btitle=Harmonices+Mundi+Libri+V&rft.place=Linz%2C+Austria&rft.pages=64&rft.pub=Sumptibus+Godofredi+Tampachii+bibl.+Francof.+excudebat+Ioannes+Plancus+%5Bpublished+by+Gottfried+Tambach+%5B...%5D+printed+by+Johann+Planck%5D&rft.date=1619&rft_id=info%3Aoclcnum%2F863358134&rft.au=Ioannis+Keppler+%5B%27%27i.e.%27%27%2C+Johannes+Kepler%5D&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fioanniskepplerih00kepl%2Fpage%2Fn87%2Fmode%2F1up&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARhombicosidodecahedron" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><i>Harmonies Of The World</i> by Johannes Kepler, Translated into English with an introduction and notes by <i>E. J. Aiton</i>, <i>A. M. Duncan</i>, <i>J. V. Field</i>, 1997, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-87169-209-0" title="Special:BookSources/0-87169-209-0">0-87169-209-0</a> (page 123)</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><span class="citation mathworld" id="Reference-Mathworld-Icosahedral_group"><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/IcosahedralGroup.html">"Icosahedral group"</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=Icosahedral+group&rft.au=Weisstein%2C+Eric+W.&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FIcosahedralGroup.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARhombicosidodecahedron" class="Z3988"></span></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><span class="citation mathworld" id="Reference-Mathworld-Zome"><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/Zome.html">"Zome"</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=Zome&rft.au=Weisstein%2C+Eric+W.&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FZome.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARhombicosidodecahedron" class="Z3988"></span></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFReadWilson1998" class="citation cs2">Read, R. C.; Wilson, R. J. (1998), <i>An Atlas of Graphs</i>, <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>, p. 269</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.pages=269&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%3ARhombicosidodecahedron" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rhombicosidodecahedron&action=edit&section=14" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilliams1979" class="citation book cs1"><a href="/wiki/Robert_Williams_(geometer)" title="Robert Williams (geometer)">Williams, Robert</a> (1979). <i>The Geometrical Foundation of Natural Structure: A Source Book of Design</i>. Dover Publications, Inc. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-486-23729-X" title="Special:BookSources/0-486-23729-X"><bdi>0-486-23729-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Geometrical+Foundation+of+Natural+Structure%3A+A+Source+Book+of+Design&rft.pub=Dover+Publications%2C+Inc&rft.date=1979&rft.isbn=0-486-23729-X&rft.aulast=Williams&rft.aufirst=Robert&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARhombicosidodecahedron" class="Z3988"></span> (Section 3-9)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCromwell,_P.1997" class="citation book cs1">Cromwell, P. (1997). <i>Polyhedra</i>. United Kingdom: Cambridge. pp. 79–86 <i>Archimedean solids</i>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-55432-2" title="Special:BookSources/0-521-55432-2"><bdi>0-521-55432-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Polyhedra&rft.place=United+Kingdom&rft.pages=79-86+%27%27Archimedean+solids%27%27&rft.pub=Cambridge&rft.date=1997&rft.isbn=0-521-55432-2&rft.au=Cromwell%2C+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARhombicosidodecahedron" class="Z3988"></span></li> <li><i><a href="/wiki/The_Big_Bang_Theory" title="The Big Bang Theory">The Big Bang Theory</a> Series 8 Episode 2 - The Junior Professor Solution</i>: features this solid as the answer to an impromptu science quiz the main four characters have in Leonard and Sheldon's apartment, and is also illustrated in <a href="/wiki/Chuck_Lorre" title="Chuck Lorre">Chuck Lorre</a>'s <b>Vanity Card #461</b> at the end of that episode.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rhombicosidodecahedron&action=edit&section=15" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <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"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/80px-Wiktionary-logo-en-v2.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span></div> <div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/Special:Search/rhombicosidodecahedron" class="extiw" title="wiktionary:Special:Search/rhombicosidodecahedron">rhombicosidodecahedron</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <ul><li><cite id="Reference-Mathworld-Small_Rhombicosidodecahedron"><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/SmallRhombicosidodecahedron.html">Small Rhombicosidodecahedron</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-Small_rhombicosidodecahedron_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/SmallRhombicosidodecahedralGraph.html">"Small rhombicosidodecahedron 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=Small+rhombicosidodecahedron+graph&rft.au=Weisstein%2C+Eric+W.&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FSmallRhombicosidodecahedralGraph.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARhombicosidodecahedron" 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 x3o5x - srid"</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+x3o5x+-+srid&rft.aulast=Klitzing&rft.aufirst=Richard&rft_id=https%3A%2F%2Fbendwavy.org%2Fklitzing%2Fdimensions%2Fpolyhedra.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARhombicosidodecahedron" 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=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&name=Rhombicosidodecahedron#applet">Editable printable net of a Rhombicosidodecahedron 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 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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_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Polyhedron_truncated_4a_max.png/90px-Polyhedron_truncated_4a_max.png" decoding="async" width="90" height="89" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Polyhedron_truncated_4a_max.png/135px-Polyhedron_truncated_4a_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/77/Polyhedron_truncated_4a_max.png/180px-Polyhedron_truncated_4a_max.png 2x" data-file-width="3927" data-file-height="3873" /></a></span><br /><a href="/wiki/Truncated_tetrahedron" title="Truncated tetrahedron">Truncated tetrahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_6_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Polyhedron_truncated_6_max.png/90px-Polyhedron_truncated_6_max.png" decoding="async" width="90" height="88" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Polyhedron_truncated_6_max.png/135px-Polyhedron_truncated_6_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/58/Polyhedron_truncated_6_max.png/180px-Polyhedron_truncated_6_max.png 2x" data-file-width="3845" data-file-height="3740" /></a></span><br /><a href="/wiki/Truncated_cube" title="Truncated cube">Truncated cube</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_8_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/Polyhedron_truncated_8_max.png/90px-Polyhedron_truncated_8_max.png" decoding="async" width="90" height="88" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/Polyhedron_truncated_8_max.png/135px-Polyhedron_truncated_8_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f4/Polyhedron_truncated_8_max.png/180px-Polyhedron_truncated_8_max.png 2x" data-file-width="3922" data-file-height="3854" /></a></span><br /><a href="/wiki/Truncated_octahedron" title="Truncated octahedron">Truncated octahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_12_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Polyhedron_truncated_12_max.png/90px-Polyhedron_truncated_12_max.png" decoding="async" width="90" height="94" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Polyhedron_truncated_12_max.png/135px-Polyhedron_truncated_12_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Polyhedron_truncated_12_max.png/180px-Polyhedron_truncated_12_max.png 2x" data-file-width="3828" data-file-height="3988" /></a></span><br /><a href="/wiki/Truncated_dodecahedron" title="Truncated dodecahedron">Truncated dodecahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_truncated_20_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Polyhedron_truncated_20_max.png/90px-Polyhedron_truncated_20_max.png" decoding="async" width="90" height="88" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Polyhedron_truncated_20_max.png/135px-Polyhedron_truncated_20_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Polyhedron_truncated_20_max.png/180px-Polyhedron_truncated_20_max.png 2x" data-file-width="3978" data-file-height="3877" /></a></span><br /><a href="/wiki/Truncated_icosahedron" title="Truncated icosahedron">Truncated icosahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_6-8_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Polyhedron_6-8_max.png/90px-Polyhedron_6-8_max.png" decoding="async" width="90" height="86" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Polyhedron_6-8_max.png/135px-Polyhedron_6-8_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Polyhedron_6-8_max.png/180px-Polyhedron_6-8_max.png 2x" data-file-width="3850" data-file-height="3680" /></a></span><br /><a href="/wiki/Cuboctahedron" title="Cuboctahedron">Cuboctahedron</a> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Polyhedron_12-20_max.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Polyhedron_12-20_max.png/90px-Polyhedron_12-20_max.png" decoding="async" width="90" height="91" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Polyhedron_12-20_max.png/135px-Polyhedron_12-20_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/04/Polyhedron_12-20_max.png/180px-Polyhedron_12-20_max.png 2x" data-file-width="3883" data-file-height="3933" /></a></span><br /><a href="/wiki/Icosidodecahedron" title="Icosidodecahedron">Icosidodecahedron</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> </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> </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 class="mw-selflink selflink">Rhombicosidodecahedron</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> </td> <td><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/90px-Polyhedron_snub_6-8_left_max.png" decoding="async" width="90" height="87" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Polyhedron_snub_6-8_left_max.png/135px-Polyhedron_snub_6-8_left_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Polyhedron_snub_6-8_left_max.png/180px-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/90px-Polyhedron_snub_6-8_right_max.png" decoding="async" width="90" height="89" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Polyhedron_snub_6-8_right_max.png/135px-Polyhedron_snub_6-8_right_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Polyhedron_snub_6-8_right_max.png/180px-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> </td></tr> <tr> <td><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/90px-Polyhedron_snub_12-20_left_max.png" decoding="async" width="90" height="91" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Polyhedron_snub_12-20_left_max.png/135px-Polyhedron_snub_12-20_left_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/Polyhedron_snub_12-20_left_max.png/180px-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/90px-Polyhedron_snub_12-20_right_max.png" decoding="async" width="90" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Polyhedron_snub_12-20_right_max.png/135px-Polyhedron_snub_12-20_right_max.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Polyhedron_snub_12-20_right_max.png/180px-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> </td></tr></tbody></table> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><style data-mw-deduplicate="TemplateStyles:r886047488">.mw-parser-output .nobold{font-weight:normal}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886047488"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886047488"></div><div role="navigation" class="navbox" aria-labelledby="Convex_polyhedra" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Convex_polyhedron_navigator" title="Template:Convex polyhedron navigator"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Convex_polyhedron_navigator" title="Template talk:Convex polyhedron navigator"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Convex_polyhedron_navigator" title="Special:EditPage/Template:Convex polyhedron navigator"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Convex_polyhedra" style="font-size:114%;margin:0 4em">Convex <a href="/wiki/Polyhedron" title="Polyhedron">polyhedra</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Platonic_solid" title="Platonic solid">Platonic solids</a> <span class="nobold">(<a href="/wiki/Regular_polyhedron" title="Regular polyhedron">regular</a>)</span></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Tetrahedron#Regular_tetrahedron" title="Tetrahedron">tetrahedron</a></li> <li><a href="/wiki/Cube" title="Cube">cube</a></li> <li><a href="/wiki/Octahedron" title="Octahedron">octahedron</a></li> <li><a href="/wiki/Regular_dodecahedron" title="Regular dodecahedron">dodecahedron</a></li> <li><a href="/wiki/Regular_icosahedron" title="Regular icosahedron">icosahedron</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Archimedean_solid" title="Archimedean solid">Archimedean solids</a><br /><span class="nobold">(<a href="/wiki/Semiregular_polyhedron" title="Semiregular polyhedron">semiregular</a> or <a href="/wiki/Uniform_polyhedron" title="Uniform polyhedron">uniform</a>)</span></div></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Truncated_tetrahedron" title="Truncated tetrahedron">truncated tetrahedron</a></li> <li><a href="/wiki/Cuboctahedron" title="Cuboctahedron">cuboctahedron</a></li> <li><a href="/wiki/Truncated_cube" title="Truncated cube">truncated cube</a></li> <li><a href="/wiki/Truncated_octahedron" title="Truncated octahedron">truncated octahedron</a></li> <li><a href="/wiki/Rhombicuboctahedron" title="Rhombicuboctahedron">rhombicuboctahedron</a></li> <li><a href="/wiki/Truncated_cuboctahedron" title="Truncated cuboctahedron">truncated cuboctahedron</a></li> <li><a href="/wiki/Snub_cube" title="Snub cube">snub cube</a></li> <li><a href="/wiki/Icosidodecahedron" title="Icosidodecahedron">icosidodecahedron</a></li> <li><a href="/wiki/Truncated_dodecahedron" title="Truncated dodecahedron">truncated dodecahedron</a></li> <li><a href="/wiki/Truncated_icosahedron" title="Truncated icosahedron">truncated icosahedron</a></li> <li><a class="mw-selflink selflink">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?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Rhombicosidodecahedron&oldid=1247951947">https://en.wikipedia.org/w/index.php?title=Rhombicosidodecahedron&oldid=1247951947</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Archimedean_solids" title="Category:Archimedean solids">Archimedean 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