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class="vector-toc-link" href="#Regular_prism"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Regular prism</span> </div> </a> <ul id="toc-Regular_prism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Uniform_prism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Uniform_prism"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Uniform prism</span> </div> </a> <ul id="toc-Uniform_prism-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Properties" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Properties"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Properties</span> </div> </a> <button aria-controls="toc-Properties-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 Properties subsection</span> </button> <ul id="toc-Properties-sublist" class="vector-toc-list"> <li id="toc-Volume" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Volume"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Volume</span> </div> </a> <ul id="toc-Volume-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Surface_area" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Surface_area"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Surface area</span> </div> </a> <ul id="toc-Surface_area-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Symmetry" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Symmetry"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Symmetry</span> </div> </a> <ul id="toc-Symmetry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Schlegel_diagrams" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Schlegel_diagrams"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Schlegel diagrams</span> </div> </a> <ul id="toc-Schlegel_diagrams-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Similar_polytopes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Similar_polytopes"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Similar polytopes</span> </div> </a> <button aria-controls="toc-Similar_polytopes-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 Similar polytopes subsection</span> </button> <ul id="toc-Similar_polytopes-sublist" class="vector-toc-list"> <li id="toc-Truncated_prism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Truncated_prism"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Truncated prism</span> </div> </a> <ul id="toc-Truncated_prism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Twisted_prism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Twisted_prism"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Twisted prism</span> </div> </a> <ul id="toc-Twisted_prism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Frustum" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Frustum"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Frustum</span> </div> </a> <ul id="toc-Frustum-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Star_prism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Star_prism"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Star prism</span> </div> </a> <ul id="toc-Star_prism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Crossed_prism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Crossed_prism"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Crossed prism</span> </div> </a> <ul id="toc-Crossed_prism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Toroidal_prism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Toroidal_prism"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.6</span> <span>Toroidal prism</span> </div> </a> <ul id="toc-Toroidal_prism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Prismatic_polytope" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Prismatic_polytope"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.7</span> <span>Prismatic polytope</span> </div> </a> <ul id="toc-Prismatic_polytope-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Uniform_prismatic_polytope" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Uniform_prismatic_polytope"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.8</span> <span>Uniform prismatic polytope</span> </div> </a> <ul id="toc-Uniform_prismatic_polytope-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-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">6</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">7</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Prism (geometry)</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 67 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-67" 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">67 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D9%86%D8%B4%D9%88%D8%B1_(%D9%87%D9%86%D8%AF%D8%B3%D8%A9)" title="منشور (هندسة) – Arabic" lang="ar" hreflang="ar" data-title="منشور (هندسة)" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Prisma_(xeometr%C3%ADa)" title="Prisma (xeometría) – Asturian" lang="ast" hreflang="ast" data-title="Prisma (xeometría)" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Prizma" title="Prizma – Azerbaijani" lang="az" hreflang="az" data-title="Prizma" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%BF%E0%A6%9C%E0%A6%AE_(%E0%A6%9C%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%AE%E0%A6%BF%E0%A6%A4%E0%A6%BF)" title="প্রিজম (জ্যামিতি) – Bangla" lang="bn" hreflang="bn" data-title="প্রিজম (জ্যামিতি)" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%B7%D0%BC%D0%B0_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F)" title="Призма (геометрия) – Bashkir" lang="ba" hreflang="ba" data-title="Призма (геометрия)" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D1%80%D1%8B%D0%B7%D0%BC%D0%B0_(%D0%B3%D0%B5%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F)" title="Прызма (геаметрыя) – Belarusian" lang="be" hreflang="be" data-title="Прызма (геаметрыя)" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%B7%D0%BC%D0%B0" title="Призма – Bulgarian" lang="bg" hreflang="bg" data-title="Призма" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Prizma" title="Prizma – Bosnian" lang="bs" hreflang="bs" data-title="Prizma" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Prisma_(geometria)" title="Prisma (geometria) – Catalan" lang="ca" hreflang="ca" data-title="Prisma (geometria)" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%B7%D0%BC%D0%B0_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8)" title="Призма (геометри) – Chuvash" lang="cv" hreflang="cv" data-title="Призма (геометри)" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Hranol" title="Hranol – Czech" lang="cs" hreflang="cs" data-title="Hranol" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-sn badge-Q70893996 mw-list-item" title=""><a href="https://sn.wikipedia.org/wiki/Zhumwi" title="Zhumwi – Shona" lang="sn" hreflang="sn" data-title="Zhumwi" data-language-autonym="ChiShona" data-language-local-name="Shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Prism_(geometreg)" title="Prism (geometreg) – Welsh" lang="cy" hreflang="cy" data-title="Prism (geometreg)" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Prisma_(Geometrie)" title="Prisma (Geometrie) – German" lang="de" hreflang="de" data-title="Prisma (Geometrie)" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Prisma" title="Prisma – Estonian" lang="et" hreflang="et" data-title="Prisma" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CF%81%CE%AF%CF%83%CE%BC%CE%B1_(%CE%B3%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1)" title="Πρίσμα (γεωμετρία) – Greek" lang="el" hreflang="el" data-title="Πρίσμα (γεωμετρία)" 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/Prisma_(geometr%C3%ADa)" title="Prisma (geometría) – Spanish" lang="es" hreflang="es" data-title="Prisma (geometría)" 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/Prismo" title="Prismo – Esperanto" lang="eo" hreflang="eo" data-title="Prismo" 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/Prisma_(geometria)" title="Prisma (geometria) – Basque" lang="eu" hreflang="eu" data-title="Prisma (geometria)" 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%85%D9%86%D8%B4%D9%88%D8%B1_(%D9%87%D9%86%D8%AF%D8%B3%D9%87)" title="منشور (هندسه) – Persian" lang="fa" hreflang="fa" data-title="منشور (هندسه)" 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/Prisme_(solide)" title="Prisme (solide) – French" lang="fr" hreflang="fr" data-title="Prisme (solide)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Priosma" title="Priosma – Irish" lang="ga" hreflang="ga" data-title="Priosma" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Prisma_(xeometr%C3%ADa)" title="Prisma (xeometría) – Galician" lang="gl" hreflang="gl" data-title="Prisma (xeometría)" 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/%EA%B0%81%EA%B8%B0%EB%91%A5" title="각기둥 – Korean" lang="ko" hreflang="ko" data-title="각기둥" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8A%D6%80%D5%AB%D5%A6%D5%B4%D5%A1" title="Պրիզմա – Armenian" lang="hy" hreflang="hy" data-title="Պրիզմա" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%9C%E0%A5%8D%E0%A4%AE_(%E0%A4%9C%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AE%E0%A4%BF%E0%A4%A4%E0%A4%BF)" title="प्रिज्म (ज्यामिति) – Hindi" lang="hi" hreflang="hi" data-title="प्रिज्म (ज्यामिति)" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Prizma" title="Prizma – Croatian" lang="hr" hreflang="hr" data-title="Prizma" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Prisma_(geometri)" title="Prisma (geometri) – Indonesian" lang="id" hreflang="id" data-title="Prisma (geometri)" 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/Prisma" title="Prisma – Italian" lang="it" hreflang="it" data-title="Prisma" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A0%D7%A1%D7%A8%D7%94_(%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94)" title="מנסרה (גאומטריה) – Hebrew" lang="he" hreflang="he" data-title="מנסרה (גאומטריה)" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Prisma_(g%C3%A9om%C3%A8tri)" title="Prisma (géomètri) – Javanese" lang="jv" hreflang="jv" data-title="Prisma (géomètri)" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9E%E1%83%A0%E1%83%98%E1%83%96%E1%83%9B%E1%83%90" title="პრიზმა – Georgian" lang="ka" hreflang="ka" data-title="პრიზმა" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%B7%D0%BC%D0%B0" title="Призма – Kazakh" lang="kk" hreflang="kk" data-title="Призма" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Prizma" title="Prizma – Latvian" lang="lv" hreflang="lv" data-title="Prizma" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Has%C3%A1b" title="Hasáb – Hungarian" lang="hu" hreflang="hu" data-title="Hasáb" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%B7%D0%BC%D0%B0_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0)" title="Призма (геометрија) – Macedonian" lang="mk" hreflang="mk" data-title="Призма (геометрија)" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mdf mw-list-item"><a href="https://mdf.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%B7%D0%BC%D0%B0%D1%81%D1%8C_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D1%81%D1%8C)" title="Призмась (геометриясь) – Moksha" lang="mdf" hreflang="mdf" data-title="Призмась (геометриясь)" data-language-autonym="Мокшень" data-language-local-name="Moksha" class="interlanguage-link-target"><span>Мокшень</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Prisma_(wiskunde)" title="Prisma (wiskunde) – Dutch" lang="nl" hreflang="nl" data-title="Prisma (wiskunde)" 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/%E8%A7%92%E6%9F%B1" title="角柱 – Japanese" lang="ja" hreflang="ja" data-title="角柱" 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-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Prisma_(Geometrii)" title="Prisma (Geometrii) – Northern Frisian" lang="frr" hreflang="frr" data-title="Prisma (Geometrii)" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Prisme_(geometri)" title="Prisme (geometri) – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Prisme (geometri)" 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/Prisme_i_geometri" title="Prisme i geometri – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Prisme i geometri" 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-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Prizma" title="Prizma – Uzbek" lang="uz" hreflang="uz" data-title="Prizma" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Graniastos%C5%82up" title="Graniastosłup – Polish" lang="pl" hreflang="pl" data-title="Graniastosłup" 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/Prisma" title="Prisma – Portuguese" lang="pt" hreflang="pt" data-title="Prisma" 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/Prism%C4%83_(geometrie)" title="Prismă (geometrie) – Romanian" lang="ro" hreflang="ro" data-title="Prismă (geometrie)" 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%9F%D1%80%D0%B8%D0%B7%D0%BC%D0%B0_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F)" title="Призма (геометрия) – Russian" lang="ru" hreflang="ru" data-title="Призма (геометрия)" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Prizmi_(gjeometri)" title="Prizmi (gjeometri) – Albanian" lang="sq" hreflang="sq" data-title="Prizmi (gjeometri)" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Prism_(geometry)" title="Prism (geometry) – Simple English" lang="en-simple" hreflang="en-simple" data-title="Prism (geometry)" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Hranol_(mnohosten)" title="Hranol (mnohosten) – Slovak" lang="sk" hreflang="sk" data-title="Hranol (mnohosten)" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Prizma" title="Prizma – Slovenian" lang="sl" hreflang="sl" data-title="Prizma" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%BE%D9%88%D8%A7%D8%B2%DA%A9_(%D8%A6%DB%95%D9%86%D8%AF%D8%A7%D8%B2%DB%95)" title="پوازک (ئەندازە) – Central Kurdish" lang="ckb" hreflang="ckb" data-title="پوازک (ئەندازە)" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%B7%D0%BC%D0%B0_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D1%81%D0%BA%D0%B0_%D1%84%D0%B8%D0%B3%D1%83%D1%80%D0%B0)" title="Призма (геометријска фигура) – Serbian" lang="sr" hreflang="sr" data-title="Призма (геометријска фигура)" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Prizma_(geometrija)" title="Prizma (geometrija) – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Prizma (geometrija)" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Prisma_(g%C3%A9om%C3%A9tri)" title="Prisma (géométri) – Sundanese" lang="su" hreflang="su" data-title="Prisma (géométri)" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/S%C3%A4rmi%C3%B6" title="Särmiö – Finnish" lang="fi" hreflang="fi" data-title="Särmiö" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Prisma_(geometri)" title="Prisma (geometri) – Swedish" lang="sv" hreflang="sv" data-title="Prisma (geometri)" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AE%95%E0%AE%AE%E0%AF%8D_(%E0%AE%B5%E0%AE%9F%E0%AE%BF%E0%AE%B5%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D)" title="பட்டகம் (வடிவவியல்) – Tamil" lang="ta" hreflang="ta" data-title="பட்டகம் (வடிவவியல்)" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%AA%E0%B0%9F%E0%B1%8D%E0%B0%9F%E0%B0%95%E0%B0%82_(%E0%B0%B0%E0%B1%87%E0%B0%96%E0%B0%BE%E0%B0%97%E0%B0%A3%E0%B0%BF%E0%B0%A4%E0%B0%82)" title="పట్టకం (రేఖాగణితం) – Telugu" lang="te" hreflang="te" data-title="పట్టకం (రేఖాగణితం)" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9B%E0%B8%A3%E0%B8%B4%E0%B8%8B%E0%B8%B6%E0%B8%A1" title="ปริซึม – Thai" lang="th" hreflang="th" data-title="ปริซึม" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%B7%D0%BC%D0%B0_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F)" title="Призма (геометрия) – Tajik" lang="tg" hreflang="tg" data-title="Призма (геометрия)" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Prizma_(geometri)" title="Prizma (geometri) – Turkish" lang="tr" hreflang="tr" data-title="Prizma (geometri)" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%B7%D0%BC%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Призма (математика) – Ukrainian" lang="uk" hreflang="uk" data-title="Призма (математика)" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%C3%ACnh_l%C4%83ng_tr%E1%BB%A5" title="Hình lăng trụ – Vietnamese" lang="vi" hreflang="vi" data-title="Hình lăng trụ" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%A3%B1%E6%9F%B1" title="棱柱 – Wu" lang="wuu" hreflang="wuu" data-title="棱柱" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%A3%B1%E6%9F%B1" title="棱柱 – Cantonese" lang="yue" hreflang="yue" data-title="棱柱" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%A3%B1%E6%9F%B1" title="棱柱 – Chinese" lang="zh" hreflang="zh" data-title="棱柱" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet 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id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Solid with 2 parallel n-gonal bases connected by n parallelograms</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox"><tbody><tr><th colspan="2" class="infobox-above" style="background:#e7dcc3">Set of uniform <span class="nowrap"><span class="texhtml mvar" style="font-style:italic;">n</span>-gonal</span> prisms</th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Hexagonal_Prism_BC.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Hexagonal_Prism_BC.svg/220px-Hexagonal_Prism_BC.svg.png" decoding="async" width="220" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Hexagonal_Prism_BC.svg/330px-Hexagonal_Prism_BC.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/31/Hexagonal_Prism_BC.svg/440px-Hexagonal_Prism_BC.svg.png 2x" data-file-width="385" data-file-height="315" /></a></span><div class="infobox-caption">Example: uniform hexagonal prism (<span class="texhtml"><i>n</i> = 6</span>)</div></td></tr><tr><th scope="row" class="infobox-label">Type</th><td class="infobox-data"><a href="/wiki/Uniform_polyhedron" title="Uniform polyhedron">uniform</a> in the sense of <a href="/wiki/Semiregular_polyhedron" title="Semiregular polyhedron">semiregular</a> polyhedron</td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Face_(geometry)" title="Face (geometry)">Faces</a></th><td class="infobox-data"><span class="texhtml">2 <i>n</i></span>-sided <a href="/wiki/Regular_polygon" title="Regular polygon">regular polygons</a><br /> <span class="texhtml mvar" style="font-style:italic;">n</span> <a href="/wiki/Square" title="Square">squares</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Edge_(geometry)" title="Edge (geometry)">Edges</a></th><td class="infobox-data"><span class="texhtml">3<i>n</i></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Vertex_(geometry)" title="Vertex (geometry)">Vertices</a></th><td class="infobox-data"><span class="texhtml">2<i>n</i></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Euler_characteristic" title="Euler characteristic">Euler char.</a></th><td class="infobox-data">2</td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Vertex_configuration" title="Vertex configuration">Vertex configuration</a></th><td class="infobox-data"><span class="texhtml">4.4.<i>n</i></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Schl%C3%A4fli_symbol" title="Schläfli symbol">Schläfli symbol</a></th><td class="infobox-data"><span class="texhtml">{<i>n</i>}×{ } </span><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><br /><span class="texhtml">t{2,<i>n</i>} </span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Conway_polyhedron_notation" title="Conway polyhedron notation">Conway notation</a></th><td class="infobox-data"><span class="texhtml">P<i>n</i></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Coxeter_diagram" class="mw-redirect" title="Coxeter diagram">Coxeter diagram</a></th><td class="infobox-data"><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_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/4/46/CDel_n.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/List_of_spherical_symmetry_groups" title="List of spherical symmetry groups">Symmetry group</a></th><td class="infobox-data"><a href="/wiki/Dihedral_symmetry_in_three_dimensions" title="Dihedral symmetry in three dimensions"><span class="texhtml">D<sub><i>n</i>h</sub>, [<i>n</i>,2], (*<i>n</i>22),</span></a> order <span class="texhtml">4<i>n</i></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Point_groups_in_three_dimensions#Rotation_groups" title="Point groups in three dimensions">Rotation group</a></th><td class="infobox-data"><span class="texhtml">D<sub><i>n</i></sub>, [<i>n</i>,2]<sup>+</sup>, (<i>n</i>22),</span> order <span class="texhtml">2<i>n</i></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Dual_polyhedron" title="Dual polyhedron">Dual polyhedron</a></th><td class="infobox-data"><a href="/wiki/Convex_polytope" title="Convex polytope">convex</a> dual-<a href="/wiki/Uniform_polyhedron" title="Uniform polyhedron">uniform</a> <span class="nowrap"><span class="texhtml mvar" style="font-style:italic;">n</span>-gonal</span> <a href="/wiki/Bipyramid" title="Bipyramid">bipyramid</a></td></tr><tr><th scope="row" class="infobox-label">Properties</th><td class="infobox-data">convex, <a href="/wiki/Regular_polygon" title="Regular polygon">regular polygon</a> faces, <a href="/wiki/Isogonal_figure" title="Isogonal figure">isogonal</a>, translated bases, sides ⊥ bases</td></tr><tr><th colspan="2" class="infobox-header" style="background:#e7dcc3"><a href="/wiki/Net_(polyhedron)" title="Net (polyhedron)">Net</a></th></tr><tr><td colspan="2" class="infobox-full-data"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Generalized_prisim_net.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/Generalized_prisim_net.svg/280px-Generalized_prisim_net.svg.png" decoding="async" width="280" height="431" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/Generalized_prisim_net.svg/420px-Generalized_prisim_net.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/27/Generalized_prisim_net.svg/560px-Generalized_prisim_net.svg.png 2x" data-file-width="688" data-file-height="1058" /></a></span></td></tr><tr><td colspan="2" class="infobox-full-data">Example: net of uniform enneagonal prism (<span class="texhtml"><i>n</i> = 9</span>)</td></tr></tbody></table> <p>In <a href="/wiki/Geometry" title="Geometry">geometry</a>, a <b>prism</b> is a <a href="/wiki/Polyhedron" title="Polyhedron">polyhedron</a> comprising an <span class="nowrap"><span class="texhtml mvar" style="font-style:italic;">n</span>-sided</span> polygon <a href="/wiki/Base_(geometry)" title="Base (geometry)">base</a>, a second base which is a <a href="/wiki/Translation_(geometry)" title="Translation (geometry)">translated</a> copy (rigidly moved without rotation) of the first, and <span class="texhtml mvar" style="font-style:italic;">n</span> other <a href="/wiki/Face_(geometry)" title="Face (geometry)">faces</a>, necessarily all <a href="/wiki/Parallelogram" title="Parallelogram">parallelograms</a>, joining <a href="/wiki/Corresponding_sides" class="mw-redirect" title="Corresponding sides">corresponding sides</a> of the two bases. All <a href="/wiki/Cross_section_(geometry)" title="Cross section (geometry)">cross-sections</a> parallel to the bases are translations of the bases. Prisms are named after their bases, e.g. a prism with a <a href="/wiki/Pentagonal" class="mw-redirect" title="Pentagonal">pentagonal</a> base is called a pentagonal prism. Prisms are a subclass of <a href="/wiki/Prismatoid" title="Prismatoid">prismatoids</a>.<sup id="cite_ref-prismatoid_2-0" class="reference"><a href="#cite_note-prismatoid-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Like many basic geometric terms, the word <i>prism</i> (from <a href="/wiki/Greek_language" title="Greek language">Greek</a> <i> </i>πρίσμα<i> (prisma)</i> 'something sawed') was first used in <a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements">Euclid's Elements</a>. Euclid defined the term in Book XI as “a solid figure contained by two opposite, equal and parallel planes, while the rest are parallelograms”. However, this definition has been criticized for not being specific enough in regard to the nature of the bases (a cause of some confusion amongst generations of later geometry writers).<sup id="cite_ref-malton-1774_3-0" class="reference"><a href="#cite_note-malton-1774-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-elliot-1845_4-0" class="reference"><a href="#cite_note-elliot-1845-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Oblique_vs_right">Oblique vs right</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism_(geometry)&action=edit&section=1" title="Edit section: Oblique vs right"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An <b>oblique prism</b> is a prism in which the joining edges and faces are <i><b>not <a href="/wiki/Perpendicular" title="Perpendicular">perpendicular</a></b></i> to the base faces. </p><p>Example: a <a href="/wiki/Parallelepiped" title="Parallelepiped">parallelepiped</a> is an oblique prism whose base is a <a href="/wiki/Parallelogram" title="Parallelogram">parallelogram</a>, or equivalently a polyhedron with six parallelogram faces. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Right_Prism.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Right_Prism.svg/220px-Right_Prism.svg.png" decoding="async" width="220" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Right_Prism.svg/330px-Right_Prism.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Right_Prism.svg/440px-Right_Prism.svg.png 2x" data-file-width="576" data-file-height="324" /></a><figcaption>Right Prism</figcaption></figure> <p>A <b><i>right</i> prism</b> is a prism in which the joining edges and faces are <i><a href="/wiki/Perpendicular" title="Perpendicular">perpendicular</a></i> to the base faces.<sup id="cite_ref-mensuration_5-0" class="reference"><a href="#cite_note-mensuration-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> This applies <a href="/wiki/If_and_only_if" title="If and only if">if and only if</a> all the joining faces are <i><a href="/wiki/Rectangular" class="mw-redirect" title="Rectangular">rectangular</a></i>. </p><p>The <a href="/wiki/Dual_polyhedron" title="Dual polyhedron">dual</a> of a <i>right</i> <span class="texhtml mvar" style="font-style:italic;">n</span>-prism is a <i>right</i> <span class="texhtml mvar" style="font-style:italic;">n</span>-<a href="/wiki/Bipyramid" title="Bipyramid">bipyramid</a>. </p><p>A right prism (with rectangular sides) with <a href="/wiki/Regular_polygon" title="Regular polygon">regular <span class="texhtml mvar" style="font-style:italic;">n</span>-gon</a> bases has Schläfli symbol <span class="texhtml">{ }×{<i>n</i>}.</span> It approaches a <a href="/wiki/Cylinder_(geometry)" class="mw-redirect" title="Cylinder (geometry)">cylinder</a> as <span class="texhtml mvar" style="font-style:italic;">n</span> approaches <a href="/wiki/Infinity" title="Infinity">infinity</a>.<sup id="cite_ref-cylinder_6-0" class="reference"><a href="#cite_note-cylinder-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Special_cases">Special cases</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism_(geometry)&action=edit&section=2" title="Edit section: Special cases"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>A right rectangular prism (with a rectangular base) is also called a <i><a href="/wiki/Cuboid" title="Cuboid">cuboid</a></i>, or informally a <i>rectangular box</i>. A right rectangular prism has <a href="/wiki/Schl%C3%A4fli_symbol" title="Schläfli symbol">Schläfli symbol</a> <span class="texhtml">{ }×{ }×{ }.</span></li> <li>A right square prism (with a square base) is also called a <i>square cuboid</i>, or informally a <i>square box</i>.</li></ul> <p>Note: some texts may apply the term <i>rectangular prism</i> or <i>square prism</i> to both a right rectangular-based prism and a right square-based prism. </p> <div class="mw-heading mw-heading2"><h2 id="Types">Types</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism_(geometry)&action=edit&section=3" title="Edit section: Types"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Regular_prism">Regular prism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism_(geometry)&action=edit&section=4" title="Edit section: Regular prism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <b>regular prism</b> is a prism with <a href="/wiki/Regular_polygon" title="Regular polygon">regular</a> bases. </p> <div class="mw-heading mw-heading3"><h3 id="Uniform_prism">Uniform prism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism_(geometry)&action=edit&section=5" title="Edit section: Uniform prism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <b>uniform prism</b> or <b>semiregular prism</b> is a right prism with regular bases and all edges of the same length. </p><p>Thus all the side faces of a uniform prism are <a href="/wiki/Square" title="Square">squares</a>. </p><p>Thus all the faces of a uniform prism are regular polygons. Also, such prisms are <a href="/wiki/Isogonal_figure" title="Isogonal figure">isogonal</a>; thus they are <a href="/wiki/Uniform_polyhedra" class="mw-redirect" title="Uniform polyhedra">uniform polyhedra</a>. They form one of the two infinite series of <a href="/wiki/Semiregular_polyhedra" class="mw-redirect" title="Semiregular polyhedra">semiregular polyhedra</a>, the other series being formed by the <a href="/wiki/Antiprism" title="Antiprism">antiprisms</a>. </p><p>A uniform <span class="texhtml mvar" style="font-style:italic;">n</span>-gonal prism has <a href="/wiki/Schl%C3%A4fli_symbol" title="Schläfli symbol">Schläfli symbol</a> <span class="texhtml">t{2,<i>n</i>}.</span> </p> <table class="wikitable mw-collapsible mw-collapsed"> <tbody><tr> <th colspan="14">Family of <a href="/wiki/Uniform_polyhedron" title="Uniform polyhedron">uniform</a> <i>n</i>-gonal <a class="mw-selflink selflink">prisms</a> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini" style="float:right;"><ul class="navbar-brackets"><li class="nv-view"><a href="/wiki/Template:UniformPrisms" title="Template:UniformPrisms"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:UniformPrisms" title="Template talk:UniformPrisms"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:UniformPrisms" title="Special:EditPage/Template:UniformPrisms"><abbr title="Edit this template">e</abbr></a></li></ul></div> </th></tr> <tr style="text-align:center;"> <th>Prism name </th> <th><a href="/wiki/Dihedron" title="Dihedron">Digonal prism</a> </th> <th>(Trigonal)<br /><a href="/wiki/Triangular_prism" title="Triangular prism">Triangular prism</a> </th> <th>(Tetragonal)<br /><a href="/wiki/Cube" title="Cube">Square prism</a> </th> <th><a href="/wiki/Pentagonal_prism" title="Pentagonal prism">Pentagonal prism</a> </th> <th><a href="/wiki/Hexagonal_prism" title="Hexagonal prism">Hexagonal prism</a> </th> <th><a href="/wiki/Heptagonal_prism" title="Heptagonal prism">Heptagonal prism</a> </th> <th><a href="/wiki/Octagonal_prism" title="Octagonal prism">Octagonal prism</a> </th> <th><a href="/wiki/Enneagonal_prism" class="mw-redirect" title="Enneagonal prism">Enneagonal prism</a> </th> <th><a href="/wiki/Decagonal_prism" class="mw-redirect" title="Decagonal prism">Decagonal prism</a> </th> <th><a href="/wiki/Hendecagonal_prism" class="mw-redirect" title="Hendecagonal prism">Hendecagonal prism</a> </th> <th><a href="/wiki/Dodecagonal_prism" title="Dodecagonal prism">Dodecagonal prism</a> </th> <th>... </th> <th><a href="/wiki/Apeirogonal_prism" title="Apeirogonal prism">Apeirogonal prism</a> </th></tr> <tr style="text-align:center;"> <th>Polyhedron image </th> <td><span typeof="mw:File"><a href="/wiki/File:Yellow_square.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c1/Yellow_square.gif" decoding="async" width="40" height="40" class="mw-file-element" data-file-width="5" data-file-height="5" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Triangular_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Triangular_prism.png/40px-Triangular_prism.png" decoding="async" width="40" height="51" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Triangular_prism.png/60px-Triangular_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/21/Triangular_prism.png/80px-Triangular_prism.png 2x" data-file-width="730" data-file-height="925" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Tetragonal_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Tetragonal_prism.png/40px-Tetragonal_prism.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Tetragonal_prism.png/60px-Tetragonal_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Tetragonal_prism.png/80px-Tetragonal_prism.png 2x" data-file-width="924" data-file-height="924" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Pentagonal_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Pentagonal_prism.png/40px-Pentagonal_prism.png" decoding="async" width="40" height="37" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Pentagonal_prism.png/60px-Pentagonal_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Pentagonal_prism.png/80px-Pentagonal_prism.png 2x" data-file-width="967" data-file-height="903" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Hexagonal_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Hexagonal_prism.png/40px-Hexagonal_prism.png" decoding="async" width="40" height="35" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Hexagonal_prism.png/60px-Hexagonal_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/25/Hexagonal_prism.png/80px-Hexagonal_prism.png 2x" data-file-width="991" data-file-height="858" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Prism_7.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Prism_7.png/40px-Prism_7.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Prism_7.png/60px-Prism_7.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Prism_7.png/80px-Prism_7.png 2x" data-file-width="1000" data-file-height="1000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Octagonal_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Octagonal_prism.png/40px-Octagonal_prism.png" decoding="async" width="40" height="31" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Octagonal_prism.png/60px-Octagonal_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/59/Octagonal_prism.png/80px-Octagonal_prism.png 2x" data-file-width="986" data-file-height="775" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Prism_9.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Prism_9.png/40px-Prism_9.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Prism_9.png/60px-Prism_9.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Prism_9.png/80px-Prism_9.png 2x" data-file-width="1000" data-file-height="898" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Decagonal_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Decagonal_prism.png/40px-Decagonal_prism.png" decoding="async" width="40" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Decagonal_prism.png/60px-Decagonal_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Decagonal_prism.png/80px-Decagonal_prism.png 2x" data-file-width="997" data-file-height="757" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Hendecagonal_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Hendecagonal_prism.png/40px-Hendecagonal_prism.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Hendecagonal_prism.png/60px-Hendecagonal_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Hendecagonal_prism.png/80px-Hendecagonal_prism.png 2x" data-file-width="1000" data-file-height="1000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dodecagonal_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Dodecagonal_prism.png/40px-Dodecagonal_prism.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Dodecagonal_prism.png/60px-Dodecagonal_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Dodecagonal_prism.png/80px-Dodecagonal_prism.png 2x" data-file-width="1000" data-file-height="1000" /></a></span> </td> <td>... </td> <td> </td></tr> <tr style="text-align:center;"> <th>Spherical tiling image </th> <td><span typeof="mw:File"><a href="/wiki/File:Spherical_digonal_prism.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Spherical_digonal_prism.svg/40px-Spherical_digonal_prism.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Spherical_digonal_prism.svg/60px-Spherical_digonal_prism.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Spherical_digonal_prism.svg/80px-Spherical_digonal_prism.svg.png 2x" data-file-width="539" data-file-height="539" /></a></span> </td> <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/40px-Spherical_triangular_prism.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Spherical_triangular_prism.svg/60px-Spherical_triangular_prism.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Spherical_triangular_prism.svg/80px-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:Spherical_square_prism.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Spherical_square_prism.svg/40px-Spherical_square_prism.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Spherical_square_prism.svg/60px-Spherical_square_prism.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Spherical_square_prism.svg/80px-Spherical_square_prism.svg.png 2x" data-file-width="577" data-file-height="577" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Spherical_pentagonal_prism.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Spherical_pentagonal_prism.svg/40px-Spherical_pentagonal_prism.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Spherical_pentagonal_prism.svg/60px-Spherical_pentagonal_prism.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Spherical_pentagonal_prism.svg/80px-Spherical_pentagonal_prism.svg.png 2x" data-file-width="577" data-file-height="577" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Spherical_hexagonal_prism.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Spherical_hexagonal_prism.svg/40px-Spherical_hexagonal_prism.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Spherical_hexagonal_prism.svg/60px-Spherical_hexagonal_prism.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Spherical_hexagonal_prism.svg/80px-Spherical_hexagonal_prism.svg.png 2x" data-file-width="577" data-file-height="577" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Spherical_heptagonal_prism.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Spherical_heptagonal_prism.svg/40px-Spherical_heptagonal_prism.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Spherical_heptagonal_prism.svg/60px-Spherical_heptagonal_prism.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Spherical_heptagonal_prism.svg/80px-Spherical_heptagonal_prism.svg.png 2x" data-file-width="577" data-file-height="577" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Spherical_octagonal_prism.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Spherical_octagonal_prism.svg/40px-Spherical_octagonal_prism.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Spherical_octagonal_prism.svg/60px-Spherical_octagonal_prism.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Spherical_octagonal_prism.svg/80px-Spherical_octagonal_prism.svg.png 2x" data-file-width="577" data-file-height="577" /></a></span> </td> <td> </td> <td><span typeof="mw:File"><a href="/wiki/File:Spherical_decagonal_prism.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Spherical_decagonal_prism.svg/40px-Spherical_decagonal_prism.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Spherical_decagonal_prism.svg/60px-Spherical_decagonal_prism.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Spherical_decagonal_prism.svg/80px-Spherical_decagonal_prism.svg.png 2x" data-file-width="577" data-file-height="577" /></a></span> </td> <td> </td> <td> </td> <th>Plane tiling image </th> <td><span typeof="mw:File"><a href="/wiki/File:Infinite_prism.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Infinite_prism.svg/80px-Infinite_prism.svg.png" decoding="async" width="80" height="35" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Infinite_prism.svg/120px-Infinite_prism.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Infinite_prism.svg/160px-Infinite_prism.svg.png 2x" data-file-width="800" data-file-height="350" /></a></span> </td></tr> <tr style="text-align:center;"> <th><a href="/wiki/Vertex_configuration" title="Vertex configuration">Vertex config.</a> </th> <td>2.4.4</td> <td>3.4.4</td> <td>4.4.4</td> <td>5.4.4</td> <td>6.4.4</td> <td>7.4.4</td> <td>8.4.4</td> <td>9.4.4</td> <td>10.4.4</td> <td>11.4.4</td> <td>12.4.4</td> <td>...</td> <td>∞.4.4 </td></tr> <tr style="text-align:center;"> <th><a href="/wiki/Coxeter_diagram" class="mw-redirect" title="Coxeter diagram">Coxeter diagram</a> </th> <td><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/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_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span></span> </td> <td><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span></span> </td> <td><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span></span> </td> <td><span 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/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span></span> </td> <td><span 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/3/32/CDel_6.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span></span> </td> <td><span 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/f/fc/CDel_7.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span></span> </td> <td><span 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/f/f7/CDel_8.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span></span> </td> <td><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/8/8a/CDel_9.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span></span> </td> <td><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/c/c6/CDel_10.png" decoding="async" width="10" height="23" class="mw-file-element" data-file-width="10" 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/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span></span> </td> <td><span 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/6/65/CDel_11.png" decoding="async" width="8" height="23" class="mw-file-element" data-file-width="8" 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/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span></span> </td> <td><span 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/0/0e/CDel_12.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/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_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span></span> </td> <td>... </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/b/be/CDel_infin.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/1/16/CDel_2.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></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Properties">Properties</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism_(geometry)&action=edit&section=6" title="Edit section: Properties"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Volume">Volume</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism_(geometry)&action=edit&section=7" title="Edit section: Volume"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Volume" title="Volume">volume</a> of a prism is the product of the <a href="/wiki/Area" title="Area">area</a> of the base by the height, i.e. the distance between the two base faces (in the case of a non-right prism, note that this means the perpendicular distance). </p><p>The volume is therefore: </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 V=Bh,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mi>B</mi> <mi>h</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V=Bh,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f754448c12a2ba6ad7d54b71174f59d9b42e9c5d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.636ex; height:2.509ex;" alt="{\displaystyle V=Bh,}"></span></dd></dl> <p>where <span class="texhtml mvar" style="font-style:italic;">B</span> is the base area and <span class="texhtml mvar" style="font-style:italic;">h</span> is the height. </p><p>The volume of a prism whose base is an <span class="texhtml mvar" style="font-style:italic;">n</span>-sided <a href="/wiki/Regular_polygon" title="Regular polygon">regular polygon</a> with side length <span class="texhtml mvar" style="font-style:italic;">s</span> is therefore: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V={\frac {n}{4}}hs^{2}\cot {\frac {\pi }{n}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>n</mi> <mn>4</mn> </mfrac> </mrow> <mi>h</mi> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>cot</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mi>n</mi> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V={\frac {n}{4}}hs^{2}\cot {\frac {\pi }{n}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f195f80e4de4453ce292e0c3c90d3b1b68cb1743" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:17.352ex; height:4.676ex;" alt="{\displaystyle V={\frac {n}{4}}hs^{2}\cot {\frac {\pi }{n}}.}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Surface_area">Surface area</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism_(geometry)&action=edit&section=8" title="Edit section: Surface area"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The surface <a href="/wiki/Area" title="Area">area</a> of a right prism is: </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 2B+Ph,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>B</mi> <mo>+</mo> <mi>P</mi> <mi>h</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2B+Ph,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac3c81a9c4ebc1d8c24dcabcc347c4b6e29088b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.498ex; height:2.509ex;" alt="{\displaystyle 2B+Ph,}"></span></dd></dl> <p>where <span class="texhtml mvar" style="font-style:italic;">B</span> is the area of the base, <span class="texhtml mvar" style="font-style:italic;">h</span> the height, and <span class="texhtml mvar" style="font-style:italic;">P</span> the base <a href="/wiki/Perimeter" title="Perimeter">perimeter</a>. </p><p>The surface area of a right prism whose base is a regular <span class="texhtml mvar" style="font-style:italic;">n</span>-sided <a href="/wiki/Polygon" title="Polygon">polygon</a> with side length <span class="texhtml mvar" style="font-style:italic;">s</span>, and with height <span class="texhtml mvar" style="font-style:italic;">h</span>, is therefore: </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 A={\frac {n}{2}}s^{2}\cot {\frac {\pi }{n}}+nsh.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>n</mi> <mn>2</mn> </mfrac> </mrow> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>cot</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mi>n</mi> </mfrac> </mrow> <mo>+</mo> <mi>n</mi> <mi>s</mi> <mi>h</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\frac {n}{2}}s^{2}\cot {\frac {\pi }{n}}+nsh.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50ab0acd64c55d17e81421d6f11a283f639339fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:22.633ex; height:4.676ex;" alt="{\displaystyle A={\frac {n}{2}}s^{2}\cot {\frac {\pi }{n}}+nsh.}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Symmetry">Symmetry</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism_(geometry)&action=edit&section=9" title="Edit section: Symmetry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Symmetry_group" title="Symmetry group">symmetry group</a> of a right <span class="texhtml mvar" style="font-style:italic;">n</span>-sided prism with regular base is <span class="texhtml"><a href="/wiki/Dihedral_group" title="Dihedral group">D<sub><i>n</i>h</sub></a></span> of order <span class="texhtml">4<i>n</i></span>, except in the case of a cube, which has the larger symmetry group <span class="texhtml"><a href="/wiki/Octahedral_symmetry" title="Octahedral symmetry">O<sub>h</sub></a></span> of order 48, which has three versions of <span class="texhtml">D<sub>4h</sub></span> as <a href="/wiki/Subgroup" title="Subgroup">subgroups</a>. The <a href="/wiki/Point_groups_in_three_dimensions#Rotation_groups" title="Point groups in three dimensions">rotation group</a> is <span class="texhtml">D<sub><i>n</i></sub></span> of order <span class="texhtml">2<i>n</i></span>, except in the case of a cube, which has the larger symmetry group <span class="texhtml">O</span> of order 24, which has three versions of <span class="texhtml">D<sub>4</sub></span> as subgroups. </p><p>The symmetry group <span class="texhtml">D<sub><i>n</i>h</sub></span> contains <a href="/wiki/Point_reflection" title="Point reflection">inversion</a> <a href="/wiki/If_and_only_if" title="If and only if">iff</a> <span class="texhtml mvar" style="font-style:italic;">n</span> is even. </p><p>The <a href="/wiki/Hosohedron" title="Hosohedron">hosohedra</a> and <a href="/wiki/Dihedron" title="Dihedron">dihedra</a> also possess dihedral symmetry, and an <span class="texhtml mvar" style="font-style:italic;">n</span>-gonal prism can be constructed via the <a href="/wiki/Truncation_(geometry)" title="Truncation (geometry)">geometrical truncation</a> of an <span class="texhtml mvar" style="font-style:italic;">n</span>-gonal hosohedron, as well as through the <a href="/wiki/Cantellation" class="mw-redirect" title="Cantellation">cantellation</a> or <a href="/wiki/Expansion_(geometry)" title="Expansion (geometry)">expansion</a> of an <span class="texhtml mvar" style="font-style:italic;">n</span>-gonal dihedron. </p> <div class="mw-heading mw-heading3"><h3 id="Schlegel_diagrams"><a href="/wiki/Schlegel_diagram" title="Schlegel diagram">Schlegel diagrams</a></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism_(geometry)&action=edit&section=10" title="Edit section: Schlegel diagrams"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr align="center"> <td><span typeof="mw:File"><a href="/wiki/File:Triangular_prismatic_graph.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Triangular_prismatic_graph.png/100px-Triangular_prismatic_graph.png" decoding="async" width="100" height="78" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Triangular_prismatic_graph.png/150px-Triangular_prismatic_graph.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/Triangular_prismatic_graph.png/200px-Triangular_prismatic_graph.png 2x" data-file-width="588" data-file-height="461" /></a></span><br />P3 </td> <td><span typeof="mw:File"><a href="/wiki/File:Cubical_graph.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Cubical_graph.png/100px-Cubical_graph.png" decoding="async" width="100" height="88" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Cubical_graph.png/150px-Cubical_graph.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Cubical_graph.png/200px-Cubical_graph.png 2x" data-file-width="474" data-file-height="417" /></a></span><br />P4 </td> <td><span typeof="mw:File"><a href="/wiki/File:Pentagonal_prismatic_graph.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Pentagonal_prismatic_graph.png/100px-Pentagonal_prismatic_graph.png" decoding="async" width="100" height="95" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Pentagonal_prismatic_graph.png/150px-Pentagonal_prismatic_graph.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Pentagonal_prismatic_graph.png/200px-Pentagonal_prismatic_graph.png 2x" data-file-width="517" data-file-height="493" /></a></span><br />P5 </td> <td><span typeof="mw:File"><a href="/wiki/File:Hexagonal_prismatic_graph.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Hexagonal_prismatic_graph.png/100px-Hexagonal_prismatic_graph.png" decoding="async" width="100" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Hexagonal_prismatic_graph.png/150px-Hexagonal_prismatic_graph.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Hexagonal_prismatic_graph.png/200px-Hexagonal_prismatic_graph.png 2x" data-file-width="480" data-file-height="434" /></a></span><br />P6 </td> <td><span typeof="mw:File"><a href="/wiki/File:Heptagonal_prismatic_graph.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Heptagonal_prismatic_graph.png/100px-Heptagonal_prismatic_graph.png" decoding="async" width="100" height="98" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Heptagonal_prismatic_graph.png/150px-Heptagonal_prismatic_graph.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Heptagonal_prismatic_graph.png/200px-Heptagonal_prismatic_graph.png 2x" data-file-width="437" data-file-height="430" /></a></span><br />P7 </td> <td><span typeof="mw:File"><a href="/wiki/File:Octagonal_prismatic_graph.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Octagonal_prismatic_graph.png/100px-Octagonal_prismatic_graph.png" decoding="async" width="100" height="101" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Octagonal_prismatic_graph.png/150px-Octagonal_prismatic_graph.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Octagonal_prismatic_graph.png/200px-Octagonal_prismatic_graph.png 2x" data-file-width="419" data-file-height="422" /></a></span><br />P8 </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Similar_polytopes">Similar polytopes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism_(geometry)&action=edit&section=11" title="Edit section: Similar polytopes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Truncated_prism">Truncated prism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism_(geometry)&action=edit&section=12" title="Edit section: Truncated prism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:TruncatedTriangularPrism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/TruncatedTriangularPrism.png/220px-TruncatedTriangularPrism.png" decoding="async" width="220" height="249" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/TruncatedTriangularPrism.png/330px-TruncatedTriangularPrism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8c/TruncatedTriangularPrism.png/440px-TruncatedTriangularPrism.png 2x" data-file-width="1203" data-file-height="1359" /></a><figcaption>Example truncated triangular prism. Its top face is truncated at an oblique angle, but it is not an <a href="#Oblique_prism">oblique prism</a>.</figcaption></figure> <p>A <b>truncated prism</b> is formed when prism is sliced by a plane that is not <a href="/wiki/Parallel_(geometry)" title="Parallel (geometry)">parallel</a> to its bases. A truncated prism's bases are not <a href="/wiki/Congruence_(geometry)" title="Congruence (geometry)">congruent</a>, and its sides are not parallelograms.<sup id="cite_ref-FOOTNOTEKernBland193881_7-0" class="reference"><a href="#cite_note-FOOTNOTEKernBland193881-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Twisted_prism">Twisted prism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism_(geometry)&action=edit&section=13" title="Edit section: Twisted prism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <b>twisted prism</b> is a nonconvex polyhedron constructed from a uniform <span class="texhtml mvar" style="font-style:italic;">n</span>-prism with each side face bisected on the square diagonal, by twisting the top, usually by <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"><span class="texhtml mvar" style="font-style:italic;">π</span></span><span class="sr-only">/</span><span class="den"><i>n</i></span></span>⁠</span> radians (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">180</span><span class="sr-only">/</span><span class="den"><i>n</i></span></span>⁠</span> degrees) in the same direction, causing sides to be concave.<sup id="cite_ref-gorini-2003_8-0" class="reference"><a href="#cite_note-gorini-2003-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>A twisted prism cannot be <a href="/wiki/Dissection_(geometry)" class="mw-redirect" title="Dissection (geometry)">dissected</a> into tetrahedra without adding new vertices. The simplest twisted prism has triangle bases and is called a <a href="/wiki/Sch%C3%B6nhardt_polyhedron" title="Schönhardt polyhedron">Schönhardt polyhedron</a>. </p><p>An <span class="texhtml mvar" style="font-style:italic;">n</span>-gonal <i>twisted prism</i> is topologically identical to the <span class="texhtml mvar" style="font-style:italic;">n</span>-gonal uniform <a href="/wiki/Antiprism" title="Antiprism">antiprism</a>, but has half the <a href="/wiki/List_of_spherical_symmetry_groups#Dihedral_symmetry" title="List of spherical symmetry groups">symmetry group</a>: <span class="texhtml">D<sub><i>n</i></sub>, [<i>n</i>,2]<sup>+</sup></span>, order <span class="texhtml">2<i>n</i></span>. It can be seen as a nonconvex antiprism, with tetrahedra removed between pairs of triangles. </p> <table class="wikitable"> <tbody><tr> <th>3-gonal </th> <th colspan="2">4-gonal </th> <th>12-gonal </th></tr> <tr align="center"> <td><span typeof="mw:File"><a href="/wiki/File:Sch%C3%B6nhardt_polyhedron.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Sch%C3%B6nhardt_polyhedron.svg/120px-Sch%C3%B6nhardt_polyhedron.svg.png" decoding="async" width="120" height="134" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Sch%C3%B6nhardt_polyhedron.svg/180px-Sch%C3%B6nhardt_polyhedron.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Sch%C3%B6nhardt_polyhedron.svg/240px-Sch%C3%B6nhardt_polyhedron.svg.png 2x" data-file-width="468" data-file-height="522" /></a></span><br /><a href="/wiki/Sch%C3%B6nhardt_polyhedron" title="Schönhardt polyhedron">Schönhardt polyhedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Twisted_square_antiprism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Twisted_square_antiprism.png/120px-Twisted_square_antiprism.png" decoding="async" width="120" height="115" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Twisted_square_antiprism.png/180px-Twisted_square_antiprism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Twisted_square_antiprism.png/240px-Twisted_square_antiprism.png 2x" data-file-width="1000" data-file-height="957" /></a></span><br />Twisted square prism </td> <td><span typeof="mw:File"><a href="/wiki/File:Square_antiprism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/29/Square_antiprism.png/120px-Square_antiprism.png" decoding="async" width="120" height="113" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/29/Square_antiprism.png/180px-Square_antiprism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/29/Square_antiprism.png/240px-Square_antiprism.png 2x" data-file-width="950" data-file-height="893" /></a></span><br /><a href="/wiki/Square_antiprism" title="Square antiprism">Square antiprism</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Twisted_dodecagonal_antiprism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Twisted_dodecagonal_antiprism.png/180px-Twisted_dodecagonal_antiprism.png" decoding="async" width="180" height="101" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Twisted_dodecagonal_antiprism.png/270px-Twisted_dodecagonal_antiprism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Twisted_dodecagonal_antiprism.png/360px-Twisted_dodecagonal_antiprism.png 2x" data-file-width="2000" data-file-height="1122" /></a></span><br />Twisted dodecagonal antiprism </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Frustum">Frustum</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism_(geometry)&action=edit&section=14" title="Edit section: Frustum"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <a href="/wiki/Frustum" title="Frustum">frustum</a> is a similar construction to a prism, with <a href="/wiki/Trapezoid" title="Trapezoid">trapezoid</a> lateral faces and differently sized top and bottom polygons. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Pentagonal_frustum.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Pentagonal_frustum.svg/220px-Pentagonal_frustum.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Pentagonal_frustum.svg/330px-Pentagonal_frustum.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/15/Pentagonal_frustum.svg/440px-Pentagonal_frustum.svg.png 2x" data-file-width="500" data-file-height="500" /></a><figcaption>Example pentagonal frustum</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Star_prism">Star prism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism_(geometry)&action=edit&section=15" title="Edit section: Star prism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Prismatic_uniform_polyhedron" title="Prismatic uniform polyhedron">Prismatic uniform polyhedron</a></div> <p>A <b>star prism</b> is a nonconvex polyhedron constructed by two identical <a href="/wiki/Star_polygon" title="Star polygon">star polygon</a> faces on the top and bottom, being parallel and offset by a distance and connected by rectangular faces. A <i>uniform star prism</i> will have <a href="/wiki/Schl%C3%A4fli_symbol" title="Schläfli symbol">Schläfli symbol</a> <span class="texhtml">{<i>p</i>/<i>q</i>} × { },</span> with <span class="texhtml mvar" style="font-style:italic;">p</span> rectangles and 2 <span class="texhtml">{<i>p</i>/<i>q</i>} </span> faces. It is topologically identical to a <span class="texhtml mvar" style="font-style:italic;">p</span>-gonal prism. </p> <table class="wikitable"> <caption>Examples </caption> <tbody><tr> <th><span class="texhtml">{ }×{ }<sub>180</sub>×{ } </span> </th> <th colspan="2"><span class="texhtml"><a href="/wiki/Truncation_(geometry)#Generalized_truncations" title="Truncation (geometry)">t<sub>a</sub></a>{3}×{ } </span> </th> <th><span class="texhtml">{5/2}×{ } </span> </th> <th><span class="texhtml">{7/2}×{ } </span> </th> <th><span class="texhtml">{7/3}×{ } </span> </th> <th><span class="texhtml">{8/3}×{ } </span> </th></tr> <tr align="center"> <td><span class="texhtml">D<sub>2h</sub></span>, order 8 </td> <td colspan="2"><span class="texhtml">D<sub>3h</sub></span>, order 12 </td> <td><span class="texhtml">D<sub>5h</sub></span>, order 20 </td> <td colspan="2"><span class="texhtml">D<sub>7h</sub></span>, order 28 </td> <td><span class="texhtml">D<sub>8h</sub></span>, order 32 </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Crossed-square_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Crossed-square_prism.png/100px-Crossed-square_prism.png" decoding="async" width="100" height="101" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Crossed-square_prism.png/150px-Crossed-square_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Crossed-square_prism.png/200px-Crossed-square_prism.png 2x" data-file-width="1828" data-file-height="1842" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Crossed_hexagonal_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Crossed_hexagonal_prism.png/100px-Crossed_hexagonal_prism.png" decoding="async" width="100" height="93" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Crossed_hexagonal_prism.png/150px-Crossed_hexagonal_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/Crossed_hexagonal_prism.png/200px-Crossed_hexagonal_prism.png 2x" data-file-width="1906" data-file-height="1777" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Crossed-unequal_hexagonal_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Crossed-unequal_hexagonal_prism.png/100px-Crossed-unequal_hexagonal_prism.png" decoding="async" width="100" height="83" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Crossed-unequal_hexagonal_prism.png/150px-Crossed-unequal_hexagonal_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Crossed-unequal_hexagonal_prism.png/200px-Crossed-unequal_hexagonal_prism.png 2x" data-file-width="2000" data-file-height="1664" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Pentagrammic_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Pentagrammic_prism.png/100px-Pentagrammic_prism.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Pentagrammic_prism.png/150px-Pentagrammic_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Pentagrammic_prism.png/200px-Pentagrammic_prism.png 2x" data-file-width="1000" data-file-height="1000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Heptagrammic_prism_7-2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Heptagrammic_prism_7-2.png/100px-Heptagrammic_prism_7-2.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Heptagrammic_prism_7-2.png/150px-Heptagrammic_prism_7-2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Heptagrammic_prism_7-2.png/200px-Heptagrammic_prism_7-2.png 2x" data-file-width="1000" data-file-height="1000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Heptagrammic_prism_7-3.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Heptagrammic_prism_7-3.png/100px-Heptagrammic_prism_7-3.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Heptagrammic_prism_7-3.png/150px-Heptagrammic_prism_7-3.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/Heptagrammic_prism_7-3.png/200px-Heptagrammic_prism_7-3.png 2x" data-file-width="1000" data-file-height="1000" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Prism_8-3.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Prism_8-3.png/100px-Prism_8-3.png" decoding="async" width="100" height="112" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Prism_8-3.png/150px-Prism_8-3.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/56/Prism_8-3.png/200px-Prism_8-3.png 2x" data-file-width="889" data-file-height="999" /></a></span> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Crossed_prism">Crossed prism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism_(geometry)&action=edit&section=16" title="Edit section: Crossed prism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <b>crossed prism</b> is a nonconvex polyhedron constructed from a prism, where the vertices of one base are <a href="/wiki/Point_reflection" title="Point reflection">inverted around the center</a> of this base (or rotated by 180°). This transforms the side rectangular faces into <a href="/wiki/Crossed_rectangle" class="mw-redirect" title="Crossed rectangle">crossed rectangles</a>. For a regular polygon base, the appearance is an <span class="texhtml mvar" style="font-style:italic;">n</span>-gonal <a href="/wiki/Hour_glass" class="mw-redirect" title="Hour glass">hour glass</a>. All oblique edges pass through a single body center. Note: no vertex is at this body centre. A crossed prism is topologically identical to an <span class="texhtml mvar" style="font-style:italic;">n</span>-gonal prism. </p> <table class="wikitable"> <caption>Examples </caption> <tbody><tr> <th><span class="texhtml">{ }×{ }<sub>180</sub>×{ }<sub>180</sub></span> </th> <th colspan="2"><span class="texhtml">t<sub>a</sub>{3}×{ }<sub>180</sub></span> </th> <th><span class="texhtml">{3}×{ }<sub>180</sub></span> </th> <th><span class="texhtml">{4}×{ }<sub>180</sub></span> </th> <th><span class="texhtml">{5}×{ }<sub>180</sub></span> </th> <th><span class="texhtml">{5/2}×{ }<sub>180</sub></span> </th> <th><span class="texhtml">{6}×{ }<sub>180</sub></span> </th></tr> <tr align="center"> <td><span class="texhtml">D<sub>2h</sub></span>, order 8 </td> <td colspan="3"><span class="texhtml">D<sub>3d</sub></span>, order 12 </td> <td><span class="texhtml">D<sub>4h</sub></span>, order 16 </td> <td colspan="2"><span class="texhtml">D<sub>5d</sub></span>, order 20 </td> <td><span class="texhtml">D<sub>6d</sub></span>, order 24 </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Crossed_crossed-square_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Crossed_crossed-square_prism.png/100px-Crossed_crossed-square_prism.png" decoding="async" width="100" height="106" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Crossed_crossed-square_prism.png/150px-Crossed_crossed-square_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/94/Crossed_crossed-square_prism.png/200px-Crossed_crossed-square_prism.png 2x" data-file-width="1796" data-file-height="1895" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Crossed_crossed-hexagonal_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Crossed_crossed-hexagonal_prism.png/100px-Crossed_crossed-hexagonal_prism.png" decoding="async" width="100" height="89" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Crossed_crossed-hexagonal_prism.png/150px-Crossed_crossed-hexagonal_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/41/Crossed_crossed-hexagonal_prism.png/200px-Crossed_crossed-hexagonal_prism.png 2x" data-file-width="1906" data-file-height="1701" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Crossed_crossed-unequal_hexagonal_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Crossed_crossed-unequal_hexagonal_prism.png/100px-Crossed_crossed-unequal_hexagonal_prism.png" decoding="async" width="100" height="72" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Crossed_crossed-unequal_hexagonal_prism.png/150px-Crossed_crossed-unequal_hexagonal_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Crossed_crossed-unequal_hexagonal_prism.png/200px-Crossed_crossed-unequal_hexagonal_prism.png 2x" data-file-width="1995" data-file-height="1445" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Crossed_triangular_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Crossed_triangular_prism.png/100px-Crossed_triangular_prism.png" decoding="async" width="100" height="112" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Crossed_triangular_prism.png/150px-Crossed_triangular_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/21/Crossed_triangular_prism.png/200px-Crossed_triangular_prism.png 2x" data-file-width="1690" data-file-height="1895" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Crossed_cube.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/45/Crossed_cube.png/100px-Crossed_cube.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/45/Crossed_cube.png/150px-Crossed_cube.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/45/Crossed_cube.png/200px-Crossed_cube.png 2x" data-file-width="1843" data-file-height="1844" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Crossed_pentagonal_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Crossed_pentagonal_prism.png/100px-Crossed_pentagonal_prism.png" decoding="async" width="100" height="85" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Crossed_pentagonal_prism.png/150px-Crossed_pentagonal_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Crossed_pentagonal_prism.png/200px-Crossed_pentagonal_prism.png 2x" data-file-width="1977" data-file-height="1682" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Crossed_pentagrammic_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Crossed_pentagrammic_prism.png/100px-Crossed_pentagrammic_prism.png" decoding="async" width="100" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Crossed_pentagrammic_prism.png/150px-Crossed_pentagrammic_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Crossed_pentagrammic_prism.png/200px-Crossed_pentagrammic_prism.png 2x" data-file-width="1659" data-file-height="1988" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Crossed2_hexagonal_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Crossed2_hexagonal_prism.png/100px-Crossed2_hexagonal_prism.png" decoding="async" width="100" height="86" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Crossed2_hexagonal_prism.png/150px-Crossed2_hexagonal_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Crossed2_hexagonal_prism.png/200px-Crossed2_hexagonal_prism.png 2x" data-file-width="1941" data-file-height="1668" /></a></span> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Toroidal_prism">Toroidal prism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism_(geometry)&action=edit&section=17" title="Edit section: Toroidal prism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <b>toroidal prism</b> is a nonconvex polyhedron like a <i>crossed prism</i>, but without bottom and top base faces, and with simple rectangular side faces closing the polyhedron. This can only be done for even-sided base polygons. These are topological tori, with <a href="/wiki/Euler_characteristic" title="Euler characteristic">Euler characteristic</a> of zero. The topological <a href="/wiki/Polyhedral_net" class="mw-redirect" title="Polyhedral net">polyhedral net</a> can be cut from two rows of a <a href="/wiki/Square_tiling" title="Square tiling">square tiling</a> (with <a href="/wiki/Vertex_configuration" title="Vertex configuration">vertex configuration</a> <span class="texhtml">4.4.4.4</span>): a band of <span class="texhtml mvar" style="font-style:italic;">n</span> squares, each attached to a <a href="/wiki/Rectangle" title="Rectangle">crossed rectangle</a>. An <span class="texhtml mvar" style="font-style:italic;">n</span>-gonal toroidal prism has <span class="texhtml">2<i>n</i></span> vertices, <span class="texhtml">2<i>n</i></span> faces: <span class="texhtml mvar" style="font-style:italic;">n</span> squares and <span class="texhtml mvar" style="font-style:italic;">n</span> crossed rectangles, and <span class="texhtml">4<i>n</i></span> edges. It is topologically <a href="/wiki/Self-dual_polyhedron" class="mw-redirect" title="Self-dual polyhedron">self-dual</a>. </p> <table class="wikitable"> <caption>Examples </caption> <tbody><tr align="center"> <td><span class="texhtml">D<sub>4h</sub></span>, order 16 </td> <td><span class="texhtml">D<sub>6h</sub></span>, order 24 </td></tr> <tr align="center"> <td><span class="texhtml"><i>V</i> = 8</span>, <span class="texhtml"><i>E</i> = 16</span>, <span class="texhtml"><i>F</i> = 8</span> </td> <td><span class="texhtml"><i>V</i> = 12</span>, <span class="texhtml"><i>E</i> = 24</span>, <span class="texhtml"><i>F</i> = 12</span> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Toroidal_square_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Toroidal_square_prism.png/100px-Toroidal_square_prism.png" decoding="async" width="100" height="106" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Toroidal_square_prism.png/150px-Toroidal_square_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Toroidal_square_prism.png/200px-Toroidal_square_prism.png 2x" data-file-width="581" data-file-height="618" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Toroidal_hexagonal_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Toroidal_hexagonal_prism.png/100px-Toroidal_hexagonal_prism.png" decoding="async" width="100" height="91" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Toroidal_hexagonal_prism.png/150px-Toroidal_hexagonal_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/28/Toroidal_hexagonal_prism.png/200px-Toroidal_hexagonal_prism.png 2x" data-file-width="630" data-file-height="571" /></a></span> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Prismatic_polytope">Prismatic polytope</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism_(geometry)&action=edit&section=18" title="Edit section: Prismatic polytope"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <i>prismatic <a href="/wiki/Polytope" title="Polytope">polytope</a></i> is a higher-dimensional generalization of a prism. An <span class="texhtml mvar" style="font-style:italic;">n</span>-dimensional prismatic polytope is constructed from two (<span class="texhtml"><i>n</i> − 1</span>)-dimensional polytopes, translated into the next dimension. </p><p>The prismatic <span class="texhtml mvar" style="font-style:italic;">n</span>-polytope elements are doubled from the (<span class="texhtml"><i>n</i> − 1</span>)-polytope elements and then creating new elements from the next lower element. </p><p>Take an <span class="texhtml mvar" style="font-style:italic;">n</span>-polytope with <span class="texhtml mvar" style="font-style:italic;">F<sub>i</sub></span> <a href="/wiki/Face_(geometry)" title="Face (geometry)"><span class="texhtml mvar" style="font-style:italic;">i</span>-face</a> elements (<span class="texhtml"><i>i</i> = 0, ..., <i>n</i></span>). Its (<span class="texhtml"><i>n</i> + 1</span>)-polytope prism will have <span class="texhtml">2<i>F<sub>i</sub></i> + <i>F</i><sub><i>i</i>−1</sub></span> <span class="texhtml mvar" style="font-style:italic;">i</span>-face elements. (With <span class="texhtml"><i>F</i><sub>−1</sub> = 0</span>, <span class="texhtml"><i>F<sub>n</sub></i> = 1</span>.) </p><p>By dimension: </p> <ul><li>Take a <a href="/wiki/Polygon" title="Polygon">polygon</a> with <span class="texhtml mvar" style="font-style:italic;">n</span> vertices, <span class="texhtml mvar" style="font-style:italic;">n</span> edges. Its prism has <span class="texhtml">2<i>n</i></span> vertices, <span class="texhtml">3<i>n</i></span> edges, and <span class="texhtml">2 + <i>n</i></span> faces.</li> <li>Take a <a href="/wiki/Polyhedron" title="Polyhedron">polyhedron</a> with <span class="texhtml mvar" style="font-style:italic;">V</span> vertices, <span class="texhtml mvar" style="font-style:italic;">E</span> edges, and <span class="texhtml mvar" style="font-style:italic;">F</span> faces. Its prism has <span class="texhtml">2<i>V</i></span> vertices, <span class="texhtml">2<i>E</i> + <i>V</i></span> edges, <span class="texhtml">2<i>F</i> + <i>E</i></span> faces, and <span class="texhtml">2 + <i>F</i></span> cells.</li> <li>Take a <a href="/wiki/Polychoron" class="mw-redirect" title="Polychoron">polychoron</a> with <span class="texhtml mvar" style="font-style:italic;">V</span> vertices, <span class="texhtml mvar" style="font-style:italic;">E</span> edges, <span class="texhtml mvar" style="font-style:italic;">F</span> faces, and <span class="texhtml mvar" style="font-style:italic;">C</span> cells. Its prism has <span class="texhtml">2<i>V</i></span> vertices, <span class="texhtml">2<i>E</i> + <i>V</i></span> edges, <span class="texhtml">2<i>F</i> + <i>E</i></span> faces, <span class="texhtml">2<i>C</i> + <i>F</i></span> cells, and <span class="texhtml">2 + <i>C</i></span> hypercells.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Uniform_prismatic_polytope">Uniform prismatic polytope</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism_(geometry)&action=edit&section=19" title="Edit section: Uniform prismatic polytope"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Uniform_4-polytope#Prismatic_uniform_4-polytopes" title="Uniform 4-polytope">Uniform 4-polytope § Prismatic_uniform 4-polytopes</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Uniform_5-polytope#Uniform_prismatic_forms" title="Uniform 5-polytope">Uniform 5-polytope § Uniform_prismatic forms</a></div> <p>A regular <span class="texhtml mvar" style="font-style:italic;">n</span>-polytope represented by <a href="/wiki/Schl%C3%A4fli_symbol" title="Schläfli symbol">Schläfli symbol</a> <span class="texhtml">{<i>p</i>,<i>q</i>,...,<i>t</i>} </span> can form a uniform prismatic (<span class="texhtml"><i>n</i> + 1</span>)-polytope represented by a <a href="/wiki/Cartesian_product" title="Cartesian product">Cartesian product</a> of <a href="/wiki/Schl%C3%A4fli_symbol#Prismatic_forms" title="Schläfli symbol">two Schläfli symbols</a>: <span class="texhtml">{<i>p</i>,<i>q</i>,...,<i>t</i>}×{ }.</span> </p><p>By dimension: </p> <ul><li>A 0-polytopic prism is a <a href="/wiki/Line_segment" title="Line segment">line segment</a>, represented by an empty <a href="/wiki/Schl%C3%A4fli_symbol" title="Schläfli symbol">Schläfli symbol</a> <span class="texhtml">{ }.</span> <dl><dd><span typeof="mw:File"><a href="/wiki/File:Complete_graph_K2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Complete_graph_K2.svg/60px-Complete_graph_K2.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Complete_graph_K2.svg/90px-Complete_graph_K2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Complete_graph_K2.svg/120px-Complete_graph_K2.svg.png 2x" data-file-width="10000" data-file-height="10000" /></a></span></dd></dl></li> <li>A 1-polytopic prism is a <a href="/wiki/Rectangle" title="Rectangle">rectangle</a>, made from 2 translated line segments. It is represented as the product Schläfli symbol <span class="texhtml">{ }×{ }.</span> If it is <a href="/wiki/Square" title="Square">square</a>, symmetry can be reduced: <span class="texhtml">{ }×{ } = {4}.</span> <dl><dd>Example: <span typeof="mw:File"><a href="/wiki/File:Square_diagonals.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Square_diagonals.svg/60px-Square_diagonals.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Square_diagonals.svg/90px-Square_diagonals.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Square_diagonals.svg/120px-Square_diagonals.svg.png 2x" data-file-width="500" data-file-height="500" /></a></span>, Square, <span class="texhtml">{ }×{ },</span> two parallel line segments, connected by two line segment <i>sides</i>.</dd></dl></li> <li>A <a href="/wiki/Polygon" title="Polygon">polygonal</a> prism is a 3-dimensional prism made from two translated polygons connected by rectangles. A regular polygon <span class="texhtml">{<i>p</i>} </span> can construct a uniform <span class="texhtml mvar" style="font-style:italic;">n</span>-gonal prism represented by the product <span class="texhtml">{<i>p</i>}×{ }.</span> If <span class="texhtml"><i>p</i> = 4</span>, with square sides symmetry it becomes a <a href="/wiki/Cube" title="Cube">cube</a>: <span class="texhtml">{4}×{ } = {4,3}.</span> <dl><dd>Example: <span typeof="mw:File"><a href="/wiki/File:Pentagonal_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Pentagonal_prism.png/60px-Pentagonal_prism.png" decoding="async" width="60" height="56" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Pentagonal_prism.png/90px-Pentagonal_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Pentagonal_prism.png/120px-Pentagonal_prism.png 2x" data-file-width="967" data-file-height="903" /></a></span>, <a href="/wiki/Pentagonal_prism" title="Pentagonal prism">Pentagonal prism</a>, <span class="texhtml">{5}×{ },</span> two parallel <a href="/wiki/Pentagon" title="Pentagon">pentagons</a> connected by 5 rectangular <i>sides</i>.</dd></dl></li> <li>A <a href="/wiki/Polyhedron" title="Polyhedron">polyhedral</a> prism is a 4-dimensional prism made from two translated polyhedra connected by 3-dimensional prism cells. A regular polyhedron <span class="texhtml">{<i>p</i>,<i>q</i>} </span> can construct the uniform polychoric prism, represented by the product <span class="texhtml">{<i>p</i>,<i>q</i>}×{ }.</span> If the polyhedron and the sides are cubes, it becomes a <a href="/wiki/Tesseract" title="Tesseract">tesseract</a>: <span class="texhtml">{4,3}×{ } = {4,3,3}.</span> <dl><dd>Example: <span typeof="mw:File"><a href="/wiki/File:Dodecahedral_prism.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Dodecahedral_prism.png/50px-Dodecahedral_prism.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Dodecahedral_prism.png/75px-Dodecahedral_prism.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Dodecahedral_prism.png/100px-Dodecahedral_prism.png 2x" data-file-width="1000" data-file-height="1000" /></a></span>, <a href="/wiki/Dodecahedral_prism" title="Dodecahedral prism">Dodecahedral prism</a>, <span class="texhtml">{5,3}×{ },</span> two parallel <a href="/wiki/Dodecahedra" class="mw-redirect" title="Dodecahedra">dodecahedra</a> connected by 12 pentagonal prism <i>sides</i>.</dd></dl></li> <li>...</li></ul> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:23,29-duoprism_stereographic_closeup.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/23%2C29-duoprism_stereographic_closeup.jpg/220px-23%2C29-duoprism_stereographic_closeup.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/23%2C29-duoprism_stereographic_closeup.jpg/330px-23%2C29-duoprism_stereographic_closeup.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/23%2C29-duoprism_stereographic_closeup.jpg/440px-23%2C29-duoprism_stereographic_closeup.jpg 2x" data-file-width="800" data-file-height="600" /></a><figcaption>A <span class="texhtml">{23}×{29} </span> duoprism, showing edges in <a href="/wiki/Stereographic_projection" title="Stereographic projection">stereographic projection</a>. The squares make a 23×29 grid <a href="/wiki/Flat_torus" class="mw-redirect" title="Flat torus">flat torus</a>.</figcaption></figure> <p>Higher order prismatic polytopes also exist as <a href="/wiki/Cartesian_product" title="Cartesian product">cartesian products</a> of any two or more polytopes. The dimension of a product polytope is the sum of the dimensions of its elements. The first examples of these exist in 4-dimensional space; they are called <a href="/wiki/Duoprism" title="Duoprism">duoprisms</a> as the product of two polygons in 4-dimensions. </p><p>Regular duoprisms are represented as <span class="texhtml">{<i>p</i>}×{<i>q</i>},</span> with <span class="texhtml mvar" style="font-style:italic;">pq</span> vertices, <span class="texhtml">2<i>pq</i></span> edges, <span class="texhtml mvar" style="font-style:italic;">pq</span> square faces, <span class="texhtml mvar" style="font-style:italic;">p</span> <span class="texhtml mvar" style="font-style:italic;">q</span>-gon faces, <span class="texhtml mvar" style="font-style:italic;">q</span> <span class="texhtml mvar" style="font-style:italic;">p</span>-gon faces, and bounded by <span class="texhtml mvar" style="font-style:italic;">p</span> <span class="texhtml mvar" style="font-style:italic;">q</span>-gonal prisms and <span class="texhtml mvar" style="font-style:italic;">q</span> <span class="texhtml mvar" style="font-style:italic;">p</span>-gonal prisms. </p><p>For example, <span class="texhtml">{4}×{4},</span> a <i>4-4 duoprism</i> is a lower symmetry form of a <a href="/wiki/Tesseract" title="Tesseract">tesseract</a>, as is <span class="texhtml">{4,3}×{ },</span> a <i>cubic prism</i>. <span class="texhtml">{4}×{4}×{ } </span> (4-4 duoprism prism), <span class="texhtml">{4,3}×{4} </span> (cube-4 duoprism) and <span class="texhtml">{4,3,3}×{ } </span> (tesseractic prism) are lower symmetry forms of a <a href="/wiki/5-cube" title="5-cube">5-cube</a>. </p> <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=Prism_(geometry)&action=edit&section=20" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Apeirogonal_prism" title="Apeirogonal prism">Apeirogonal prism</a></li> <li><a href="/wiki/Rectified_prism" title="Rectified prism">Rectified prism</a></li> <li><a href="/wiki/Prismanes" title="Prismanes">Prismanes</a></li> <li><a href="/wiki/List_of_shapes" class="mw-redirect" title="List of shapes">List of shapes</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism_(geometry)&action=edit&section=21" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><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="CITEREFJohnson2018" class="citation book cs1"><a href="/wiki/Norman_Johnson_(mathematician)" title="Norman Johnson (mathematician)">Johnson, N. W</a> (2018). "Chapter 11: Finite symmetry groups". <a rel="nofollow" class="external text" href="https://books.google.com/books?id=adBVDwAAQBAJ&pg=PA223"><i>Geometries and Transformations</i></a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-107-10340-5" title="Special:BookSources/978-1-107-10340-5"><bdi>978-1-107-10340-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapter+11%3A+Finite+symmetry+groups&rft.btitle=Geometries+and+Transformations&rft.date=2018&rft.isbn=978-1-107-10340-5&rft.aulast=Johnson&rft.aufirst=N.+W&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DadBVDwAAQBAJ%26pg%3DPA223&rfr_id=info%3Asid%2Fen.wikipedia.org%3APrism+%28geometry%29" class="Z3988"></span> See 11.3 Pyramids, Prisms, and Antiprisms, Figure 11.3b.</span> </li> <li id="cite_note-prismatoid-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-prismatoid_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrünbaum1997" class="citation journal cs1">Grünbaum, Branko (1997). <a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FPL00009307">"Isogonal Prismatoids"</a>. <i>Discrete & Computational Geometry</i>. <b>18</b>: 13–52. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FPL00009307">10.1007/PL00009307</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Discrete+%26+Computational+Geometry&rft.atitle=Isogonal+Prismatoids&rft.volume=18&rft.pages=13-52&rft.date=1997&rft_id=info%3Adoi%2F10.1007%2FPL00009307&rft.aulast=Gr%C3%BCnbaum&rft.aufirst=Branko&rft_id=https%3A%2F%2Fdoi.org%2F10.1007%252FPL00009307&rfr_id=info%3Asid%2Fen.wikipedia.org%3APrism+%28geometry%29" class="Z3988"></span></span> </li> <li id="cite_note-malton-1774-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-malton-1774_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMalton1774" class="citation book cs1">Malton, Thomas (1774). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=-3tLfuCB97AC&pg=PA360"><i>A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the Mathematics</i></a>. author, and sold. p. 360.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Royal+Road+to+Geometry%3A+Or%2C+an+Easy+and+Familiar+Introduction+to+the+Mathematics&rft.pages=360&rft.pub=author%2C+and+sold&rft.date=1774&rft.aulast=Malton&rft.aufirst=Thomas&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D-3tLfuCB97AC%26pg%3DPA360&rfr_id=info%3Asid%2Fen.wikipedia.org%3APrism+%28geometry%29" class="Z3988"></span></span> </li> <li id="cite_note-elliot-1845-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-elliot-1845_4-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFElliot1845" class="citation book cs1">Elliot, James (1845). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=qilLAAAAYAAJ&pg=PA3"><i>Key to the Complete Treatise on Practical Geometry and Mensuration: Containing Full Demonstrations of the Rules</i></a>. Longman, Brown, Green, and Longmans. p. 3.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Key+to+the+Complete+Treatise+on+Practical+Geometry+and+Mensuration%3A+Containing+Full+Demonstrations+of+the+Rules&rft.pages=3&rft.pub=Longman%2C+Brown%2C+Green%2C+and+Longmans&rft.date=1845&rft.aulast=Elliot&rft.aufirst=James&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DqilLAAAAYAAJ%26pg%3DPA3&rfr_id=info%3Asid%2Fen.wikipedia.org%3APrism+%28geometry%29" class="Z3988"></span></span> </li> <li id="cite_note-mensuration-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-mensuration_5-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKernBland1938" class="citation book cs1">Kern, William F.; Bland, James R. (1938). <i>Solid Mensuration with proofs</i>. p. 28.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Solid+Mensuration+with+proofs&rft.pages=28&rft.date=1938&rft.aulast=Kern&rft.aufirst=William+F.&rft.au=Bland%2C+James+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APrism+%28geometry%29" class="Z3988"></span></span> </li> <li id="cite_note-cylinder-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-cylinder_6-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGeretschlager2020" class="citation book cs1">Geretschlager, Robert (2020). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=2O_CDwAAQBAJ&pg=PA39"><i>Engaging Young Students In Mathematics Through Competitions: World Perspectives And Practices</i></a>. Vol. 1. <a href="/wiki/World_Scientific" title="World Scientific">World Scientific</a>. p. 39. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-981-120-582-8" title="Special:BookSources/978-981-120-582-8"><bdi>978-981-120-582-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Engaging+Young+Students+In+Mathematics+Through+Competitions%3A+World+Perspectives+And+Practices&rft.pages=39&rft.pub=World+Scientific&rft.date=2020&rft.isbn=978-981-120-582-8&rft.aulast=Geretschlager&rft.aufirst=Robert&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D2O_CDwAAQBAJ%26pg%3DPA39&rfr_id=info%3Asid%2Fen.wikipedia.org%3APrism+%28geometry%29" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEKernBland193881-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEKernBland193881_7-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKernBland1938">Kern & Bland (1938)</a>, p. 81.</span> </li> <li id="cite_note-gorini-2003-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-gorini-2003_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGorini2003" class="citation book cs1">Gorini, Catherine A. (2003). <a rel="nofollow" class="external text" href="https://archive.org/details/factsonfilegeome0000gori/page/172/mode/2up"><i>The facts on file: Geometry handbook</i></a>. p. 172. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8160-4875-4" title="Special:BookSources/0-8160-4875-4"><bdi>0-8160-4875-4</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+facts+on+file%3A+Geometry+handbook&rft.pages=172&rft.date=2003&rft.isbn=0-8160-4875-4&rft.aulast=Gorini&rft.aufirst=Catherine+A.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ffactsonfilegeome0000gori%2Fpage%2F172%2Fmode%2F2up&rfr_id=info%3Asid%2Fen.wikipedia.org%3APrism+%28geometry%29" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.korthalsaltes.com/cuadros.php?type=twisted-prisms">"Pictures of Twisted Prisms"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Pictures+of+Twisted+Prisms&rft_id=http%3A%2F%2Fwww.korthalsaltes.com%2Fcuadros.php%3Ftype%3Dtwisted-prisms&rfr_id=info%3Asid%2Fen.wikipedia.org%3APrism+%28geometry%29" class="Z3988"></span></span> </li> </ol></div></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAnthony_Pugh1976" class="citation book cs1">Anthony Pugh (1976). <i>Polyhedra: A visual approach</i>. California: University of California Press Berkeley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-520-03056-7" title="Special:BookSources/0-520-03056-7"><bdi>0-520-03056-7</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%3A+A+visual+approach&rft.place=California&rft.pub=University+of+California+Press+Berkeley&rft.date=1976&rft.isbn=0-520-03056-7&rft.au=Anthony+Pugh&rfr_id=info%3Asid%2Fen.wikipedia.org%3APrism+%28geometry%29" class="Z3988"></span> Chapter 2: Archimedean polyhedra, prisma and antiprisms</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=Prism_(geometry)&action=edit&section=22" 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/4/4c/Wikisource-logo.svg/38px-Wikisource-logo.svg.png" decoding="async" width="38" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/57px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/76px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></span></span></div> <div class="side-box-text plainlist"><a href="/wiki/Wikisource" title="Wikisource">Wikisource</a> has the text of the <a href="/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition" title="Encyclopædia Britannica Eleventh Edition">1911 <i>Encyclopædia Britannica</i></a> article "<span style="font-weight:bold;"><a href="https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Prism" class="extiw" title="wikisource:1911 Encyclopædia Britannica/Prism">Prism</a></span>".</div></div> </div> <ul><li><span class="citation mathworld" id="Reference-Mathworld-Prism"><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/Prism.html">"Prism"</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=Prism&rft.au=Weisstein%2C+Eric+W.&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FPrism.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3APrism+%28geometry%29" class="Z3988"></span></span></li> <li><a rel="nofollow" class="external text" href="http://www.korthalsaltes.com/selecion.php?sl=selecion3">Paper models of prisms and antiprisms</a> Free nets of prisms and antiprisms</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20141019220935/http://www.software3d.com/Prisms.php">Paper models of prisms and antiprisms</a> Using nets generated by <i><a href="/wiki/Stella_(software)" title="Stella (software)">Stella</a></i></li></ul> 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.navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style><style data-mw-deduplicate="TemplateStyles:r886047488">.mw-parser-output .nobold{font-weight:normal}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886047488"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886047488"></div><div role="navigation" class="navbox" aria-labelledby="Convex_polyhedra" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Convex_polyhedron_navigator" title="Template:Convex polyhedron navigator"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Convex_polyhedron_navigator" title="Template talk:Convex polyhedron navigator"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Convex_polyhedron_navigator" title="Special:EditPage/Template:Convex polyhedron navigator"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Convex_polyhedra" style="font-size:114%;margin:0 4em">Convex <a href="/wiki/Polyhedron" title="Polyhedron">polyhedra</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Platonic_solid" title="Platonic solid">Platonic solids</a> <span class="nobold">(<a href="/wiki/Regular_polyhedron" title="Regular polyhedron">regular</a>)</span></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Tetrahedron#Regular_tetrahedron" title="Tetrahedron">tetrahedron</a></li> <li><a href="/wiki/Cube" title="Cube">cube</a></li> <li><a href="/wiki/Octahedron" title="Octahedron">octahedron</a></li> <li><a href="/wiki/Regular_dodecahedron" title="Regular dodecahedron">dodecahedron</a></li> <li><a href="/wiki/Regular_icosahedron" title="Regular icosahedron">icosahedron</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Archimedean_solid" title="Archimedean solid">Archimedean solids</a><br /><span class="nobold">(<a href="/wiki/Semiregular_polyhedron" title="Semiregular polyhedron">semiregular</a> or <a href="/wiki/Uniform_polyhedron" title="Uniform polyhedron">uniform</a>)</span></div></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Truncated_tetrahedron" title="Truncated tetrahedron">truncated tetrahedron</a></li> <li><a href="/wiki/Cuboctahedron" title="Cuboctahedron">cuboctahedron</a></li> <li><a href="/wiki/Truncated_cube" title="Truncated cube">truncated cube</a></li> <li><a href="/wiki/Truncated_octahedron" title="Truncated octahedron">truncated octahedron</a></li> <li><a href="/wiki/Rhombicuboctahedron" title="Rhombicuboctahedron">rhombicuboctahedron</a></li> <li><a href="/wiki/Truncated_cuboctahedron" title="Truncated cuboctahedron">truncated cuboctahedron</a></li> <li><a href="/wiki/Snub_cube" title="Snub cube">snub cube</a></li> <li><a href="/wiki/Icosidodecahedron" title="Icosidodecahedron">icosidodecahedron</a></li> <li><a href="/wiki/Truncated_dodecahedron" title="Truncated dodecahedron">truncated dodecahedron</a></li> <li><a href="/wiki/Truncated_icosahedron" title="Truncated icosahedron">truncated icosahedron</a></li> <li><a href="/wiki/Rhombicosidodecahedron" title="Rhombicosidodecahedron">rhombicosidodecahedron</a></li> <li><a href="/wiki/Truncated_icosidodecahedron" title="Truncated icosidodecahedron">truncated icosidodecahedron</a></li> <li><a href="/wiki/Snub_dodecahedron" title="Snub dodecahedron">snub dodecahedron</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Catalan_solid" title="Catalan solid">Catalan solids</a><br /><span class="nobold">(duals of Archimedean)</span></div></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a 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 class="mw-selflink selflink">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 class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link 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