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class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Projekt"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Obsah" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Obsah</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">přesunout do postranního panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skrýt</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(úvod)</div> </a> </li> <li id="toc-Tabulka_vlastností_platónských_těles" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tabulka_vlastností_platónských_těles"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Tabulka vlastností platónských těles</span> </div> </a> <ul id="toc-Tabulka_vlastností_platónských_těles-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dualismus" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Dualismus"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Dualismus</span> </div> </a> <ul id="toc-Dualismus-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Historie" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Historie"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Historie</span> </div> </a> <ul id="toc-Historie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Přírodní_vědy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Přírodní_vědy"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Přírodní vědy</span> </div> </a> <ul id="toc-Přírodní_vědy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vyšší_dimenze" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Vyšší_dimenze"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Vyšší dimenze</span> </div> </a> <ul id="toc-Vyšší_dimenze-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Odkazy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Odkazy"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Odkazy</span> </div> </a> <button aria-controls="toc-Odkazy-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>Přepnout podsekci Odkazy</span> </button> <ul id="toc-Odkazy-sublist" class="vector-toc-list"> <li id="toc-Poznámky" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Poznámky"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Poznámky</span> </div> </a> <ul id="toc-Poznámky-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reference" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Reference"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Reference</span> </div> </a> <ul id="toc-Reference-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Související_články" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Související_články"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Související články</span> </div> </a> <ul id="toc-Související_články-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Externí_odkazy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Externí_odkazy"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>Externí odkazy</span> </div> </a> <ul id="toc-Externí_odkazy-sublist" class="vector-toc-list"> </ul> </li> </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="Obsah" 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="Přepnout obsah" > <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">Přepnout obsah</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">Platónské těleso</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="Přejděte k článku v jiném jazyce. Je dostupný v 59 jazycích" > <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-59" 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">59 jazyků</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Platoniese_vaste_liggaam" title="Platoniese vaste liggaam – afrikánština" lang="af" hreflang="af" data-title="Platoniese vaste liggaam" data-language-autonym="Afrikaans" data-language-local-name="afrikánština" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%AC%D8%B3%D9%85_%D8%A3%D9%81%D9%84%D8%A7%D8%B7%D9%88%D9%86%D9%8A" title="مجسم أفلاطوني – arabština" lang="ar" hreflang="ar" data-title="مجسم أفلاطوني" data-language-autonym="العربية" data-language-local-name="arabština" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/D%C3%BCzg%C3%BCn_%C3%A7ox%C3%BCzl%C3%BCl%C9%99r" title="Düzgün çoxüzlülər – ázerbájdžánština" lang="az" hreflang="az" data-title="Düzgün çoxüzlülər" data-language-autonym="Azərbaycanca" data-language-local-name="ázerbájdžánština" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Platonikong_solido" title="Platonikong solido – Central Bikol" lang="bcl" hreflang="bcl" data-title="Platonikong solido" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D0%BB%D0%B0%D1%82%D0%BE%D0%BD%D0%BE%D0%B2%D0%BE_%D1%82%D1%8F%D0%BB%D0%BE" title="Платоново тяло – bulharština" lang="bg" hreflang="bg" data-title="Платоново тяло" data-language-autonym="Български" data-language-local-name="bulharština" class="interlanguage-link-target"><span>Български</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%B2%E0%A7%87%E0%A6%9F%E0%A7%8B%E0%A6%A8%E0%A7%80%E0%A6%AF%E0%A6%BC_%E0%A6%98%E0%A6%A8%E0%A6%AC%E0%A6%B8%E0%A7%8D%E0%A6%A4%E0%A7%81" title="প্লেটোনীয় ঘনবস্তু – bengálština" lang="bn" hreflang="bn" data-title="প্লেটোনীয় ঘনবস্তু" data-language-autonym="বাংলা" data-language-local-name="bengálština" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/S%C3%B2lid_plat%C3%B2nic" title="Sòlid platònic – katalánština" lang="ca" hreflang="ca" data-title="Sòlid platònic" data-language-autonym="Català" data-language-local-name="katalánština" 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%A2%C4%95%D1%80%C4%95%D1%81_%D0%BD%D1%83%D0%BC%D0%B0%D0%B9%D1%85%D1%8B%D1%81%D0%B0%D0%BA%D0%BB%C4%83%D1%85" title="Тĕрĕс нумайхысаклăх – čuvaština" lang="cv" hreflang="cv" data-title="Тĕрĕс нумайхысаклăх" data-language-autonym="Чӑвашла" data-language-local-name="čuvaština" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Platonisk_legeme" title="Platonisk legeme – dánština" lang="da" hreflang="da" data-title="Platonisk legeme" data-language-autonym="Dansk" data-language-local-name="dánština" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Platonischer_K%C3%B6rper" title="Platonischer Körper – němčina" lang="de" hreflang="de" data-title="Platonischer Körper" data-language-autonym="Deutsch" data-language-local-name="němčina" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CE%BB%CE%B1%CF%84%CF%89%CE%BD%CE%B9%CE%BA%CF%8C_%CF%83%CF%84%CE%B5%CF%81%CE%B5%CF%8C" title="Πλατωνικό στερεό – řečtina" lang="el" hreflang="el" data-title="Πλατωνικό στερεό" data-language-autonym="Ελληνικά" data-language-local-name="řečtina" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Platonic_solid" title="Platonic solid – angličtina" lang="en" hreflang="en" data-title="Platonic solid" data-language-autonym="English" data-language-local-name="angličtina" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Platona_solido" title="Platona solido – esperanto" lang="eo" hreflang="eo" data-title="Platona solido" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/S%C3%B3lidos_plat%C3%B3nicos" title="Sólidos platónicos – španělština" lang="es" hreflang="es" data-title="Sólidos platónicos" data-language-autonym="Español" data-language-local-name="španělština" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Solido_platoniko" title="Solido platoniko – baskičtina" lang="eu" hreflang="eu" data-title="Solido platoniko" data-language-autonym="Euskara" data-language-local-name="baskičtina" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa badge-Q17437798 badge-goodarticle mw-list-item" title="dobrý článek"><a href="https://fa.wikipedia.org/wiki/%D8%AC%D8%B3%D9%85_%D8%A7%D9%81%D9%84%D8%A7%D8%B7%D9%88%D9%86%DB%8C" title="جسم افلاطونی – perština" lang="fa" hreflang="fa" data-title="جسم افلاطونی" data-language-autonym="فارسی" data-language-local-name="perština" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Platonin_kappale" title="Platonin kappale – finština" lang="fi" hreflang="fi" data-title="Platonin kappale" data-language-autonym="Suomi" data-language-local-name="finština" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Solide_de_Platon" title="Solide de Platon – francouzština" lang="fr" hreflang="fr" data-title="Solide de Platon" data-language-autonym="Français" data-language-local-name="francouzština" 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/Solad_plat%C3%B3nach" title="Solad platónach – irština" lang="ga" hreflang="ga" data-title="Solad platónach" data-language-autonym="Gaeilge" data-language-local-name="irština" 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/S%C3%B3lido_plat%C3%B3nico" title="Sólido platónico – galicijština" lang="gl" hreflang="gl" data-title="Sólido platónico" data-language-autonym="Galego" data-language-local-name="galicijština" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A4%D7%90%D7%95%D7%9F_%D7%9E%D7%A9%D7%95%D7%9B%D7%9C%D7%9C" title="פאון משוכלל – hebrejština" lang="he" hreflang="he" data-title="פאון משוכלל" data-language-autonym="עברית" data-language-local-name="hebrejština" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Szab%C3%A1lyos_test" title="Szabályos test – maďarština" lang="hu" hreflang="hu" data-title="Szabályos test" data-language-autonym="Magyar" data-language-local-name="maďarština" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BF%D5%A1%D5%B6%D5%B8%D5%B6%D5%A1%D5%BE%D5%B8%D6%80_%D5%A2%D5%A1%D5%A6%D5%B4%D5%A1%D5%B6%D5%AB%D5%BD%D5%BF" title="Կանոնավոր բազմանիստ – arménština" lang="hy" hreflang="hy" data-title="Կանոնավոր բազմանիստ" data-language-autonym="Հայերեն" data-language-local-name="arménština" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Solido_platonic" title="Solido platonic – interlingua" lang="ia" hreflang="ia" data-title="Solido platonic" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Bangun_ruang_Platonik" title="Bangun ruang Platonik – indonéština" lang="id" hreflang="id" data-title="Bangun ruang Platonik" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonéština" 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/Solido_platonico" title="Solido platonico – italština" lang="it" hreflang="it" data-title="Solido platonico" data-language-autonym="Italiano" data-language-local-name="italština" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%AD%A3%E5%A4%9A%E9%9D%A2%E4%BD%93" title="正多面体 – japonština" lang="ja" hreflang="ja" data-title="正多面体" data-language-autonym="日本語" data-language-local-name="japonština" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9E%E1%83%9A%E1%83%90%E1%83%A2%E1%83%9D%E1%83%9C%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%A1%E1%83%AE%E1%83%94%E1%83%A3%E1%83%9A%E1%83%94%E1%83%91%E1%83%98" title="პლატონური სხეულები – gruzínština" lang="ka" hreflang="ka" data-title="პლატონური სხეულები" data-language-autonym="ქართული" data-language-local-name="gruzínština" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A0%95%EB%8B%A4%EB%A9%B4%EC%B2%B4" title="정다면체 – korejština" lang="ko" hreflang="ko" data-title="정다면체" data-language-autonym="한국어" data-language-local-name="korejština" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Corpus_Platonicum" title="Corpus Platonicum – latina" lang="la" hreflang="la" data-title="Corpus Platonicum" data-language-autonym="Latina" data-language-local-name="latina" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Platono_k%C5%ABnas" title="Platono kūnas – litevština" lang="lt" hreflang="lt" data-title="Platono kūnas" data-language-autonym="Lietuvių" data-language-local-name="litevština" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Regelmatig_veelvlak" title="Regelmatig veelvlak – nizozemština" lang="nl" hreflang="nl" data-title="Regelmatig veelvlak" data-language-autonym="Nederlands" data-language-local-name="nizozemština" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Platonsk_lekam" title="Platonsk lekam – norština (nynorsk)" lang="nn" hreflang="nn" data-title="Platonsk lekam" data-language-autonym="Norsk nynorsk" data-language-local-name="norština (nynorsk)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Platonsk_legeme" title="Platonsk legeme – norština (bokmål)" lang="nb" hreflang="nb" data-title="Platonsk legeme" data-language-autonym="Norsk bokmål" data-language-local-name="norština (bokmål)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Solid_platonic" title="Solid platonic – okcitánština" lang="oc" hreflang="oc" data-title="Solid platonic" data-language-autonym="Occitan" data-language-local-name="okcitánština" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Wielo%C5%9Bcian_foremny" title="Wielościan foremny – polština" lang="pl" hreflang="pl" data-title="Wielościan foremny" data-language-autonym="Polski" data-language-local-name="polština" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/S%C3%B2lid_%C3%ABd_Platon" title="Sòlid ëd Platon – piemonština" lang="pms" hreflang="pms" data-title="Sòlid ëd Platon" data-language-autonym="Piemontèis" data-language-local-name="piemonština" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/S%C3%B3lido_plat%C3%B3nico" title="Sólido platónico – portugalština" lang="pt" hreflang="pt" data-title="Sólido platónico" data-language-autonym="Português" data-language-local-name="portugalština" 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/Poliedru_platonic" title="Poliedru platonic – rumunština" lang="ro" hreflang="ro" data-title="Poliedru platonic" data-language-autonym="Română" data-language-local-name="rumunština" 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%B0%D0%B2%D0%B8%D0%BB%D1%8C%D0%BD%D1%8B%D0%B9_%D0%BC%D0%BD%D0%BE%D0%B3%D0%BE%D0%B3%D1%80%D0%B0%D0%BD%D0%BD%D0%B8%D0%BA" title="Правильный многогранник – ruština" lang="ru" hreflang="ru" data-title="Правильный многогранник" data-language-autonym="Русский" data-language-local-name="ruština" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Platonic_solid" title="Platonic solid – skotština" lang="sco" hreflang="sco" data-title="Platonic solid" data-language-autonym="Scots" data-language-local-name="skotština" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Pravilni_poliedri" title="Pravilni poliedri – srbochorvatština" lang="sh" hreflang="sh" data-title="Pravilni poliedri" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srbochorvatština" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Platonic_solid" title="Platonic solid – Simple English" lang="en-simple" hreflang="en-simple" data-title="Platonic solid" 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/Plat%C3%B3nske_teleso" title="Platónske teleso – slovenština" lang="sk" hreflang="sk" data-title="Platónske teleso" data-language-autonym="Slovenčina" data-language-local-name="slovenština" 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/Platonsko_telo" title="Platonsko telo – slovinština" lang="sl" hreflang="sl" data-title="Platonsko telo" data-language-autonym="Slovenščina" data-language-local-name="slovinština" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Trupat_e_Platonit" title="Trupat e Platonit – albánština" lang="sq" hreflang="sq" data-title="Trupat e Platonit" data-language-autonym="Shqip" data-language-local-name="albánština" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D1%80%D0%B0%D0%B2%D0%B8%D0%BB%D0%BD%D0%B8_%D0%BF%D0%BE%D0%BB%D0%B8%D0%B5%D0%B4%D1%80%D0%B8" title="Правилни полиедри – srbština" lang="sr" hreflang="sr" data-title="Правилни полиедри" data-language-autonym="Српски / srpski" data-language-local-name="srbština" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Platonska_kroppar" title="Platonska kroppar – švédština" lang="sv" hreflang="sv" data-title="Platonska kroppar" data-language-autonym="Svenska" data-language-local-name="švédština" 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%BF%E0%AE%B3%E0%AF%87%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AF%8B%E0%AE%B5%E0%AE%BF%E0%AE%A9%E0%AF%8D_%E0%AE%9A%E0%AF%80%E0%AE%B0%E0%AF%8D%E0%AE%A4%E0%AE%BF%E0%AE%A3%E0%AF%8D%E0%AE%AE%E0%AE%99%E0%AF%8D%E0%AE%95%E0%AE%B3%E0%AF%8D" title="பிளேட்டோவின் சீர்திண்மங்கள் – tamilština" lang="ta" hreflang="ta" data-title="பிளேட்டோவின் சீர்திண்மங்கள்" data-language-autonym="தமிழ்" data-language-local-name="tamilština" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%97%E0%B8%A3%E0%B8%87%E0%B8%95%E0%B8%B1%E0%B8%99%E0%B9%80%E0%B8%9E%E0%B8%A5%E0%B9%82%E0%B8%95" title="ทรงตันเพลโต – thajština" lang="th" hreflang="th" data-title="ทรงตันเพลโต" data-language-autonym="ไทย" data-language-local-name="thajština" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Platonik_cisim" title="Platonik cisim – turečtina" lang="tr" hreflang="tr" data-title="Platonik cisim" data-language-autonym="Türkçe" data-language-local-name="turečtina" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A2%D3%A9%D0%B7%D0%B5%D0%BA_%D0%BA%D2%AF%D0%BF%D0%BA%D1%8B%D1%80%D0%BB%D1%8B%D0%BA" title="Төзек күпкырлык – tatarština" lang="tt" hreflang="tt" data-title="Төзек күпкырлык" data-language-autonym="Татарча / tatarça" data-language-local-name="tatarština" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D1%80%D0%B0%D0%B2%D0%B8%D0%BB%D1%8C%D0%BD%D0%B8%D0%B9_%D0%BC%D0%BD%D0%BE%D0%B3%D0%BE%D0%B3%D1%80%D0%B0%D0%BD%D0%BD%D0%B8%D0%BA" title="Правильний многогранник – ukrajinština" lang="uk" hreflang="uk" data-title="Правильний многогранник" data-language-autonym="Українська" data-language-local-name="ukrajinština" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A7%D9%81%D9%84%D8%A7%D8%B7%D9%88%D9%86%DB%8C_%D9%B9%DA%BE%D9%88%D8%B3" title="افلاطونی ٹھوس – urdština" lang="ur" hreflang="ur" data-title="افلاطونی ٹھوس" data-language-autonym="اردو" data-language-local-name="urdština" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Kh%E1%BB%91i_%C4%91a_di%E1%BB%87n_%C4%91%E1%BB%81u_Platon" title="Khối đa diện đều Platon – vietnamština" lang="vi" hreflang="vi" data-title="Khối đa diện đều Platon" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamština" 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%9F%8F%E6%8B%89%E5%9B%BE%E7%AB%8B%E4%BD%93" title="柏拉图立体 – čínština (dialekty Wu)" lang="wuu" hreflang="wuu" data-title="柏拉图立体" data-language-autonym="吴语" data-language-local-name="čínština (dialekty Wu)" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%9F%8F%E6%8B%89%E5%9C%96%E7%AB%8B%E9%AB%94" title="柏拉圖立體 – čínština" lang="zh" hreflang="zh" data-title="柏拉圖立體" data-language-autonym="中文" data-language-local-name="čínština" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Chi%C3%A0%E2%81%BF_to-bi%C4%81n-th%C3%A9" title="Chiàⁿ to-biān-thé – čínština (dialekty Minnan)" lang="nan" hreflang="nan" data-title="Chiàⁿ to-biān-thé" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="čínština (dialekty Minnan)" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%9F%8F%E6%8B%89%E5%9C%96%E5%A4%9A%E9%9D%A2%E9%AB%94" title="柏拉圖多面體 – kantonština" lang="yue" hreflang="yue" data-title="柏拉圖多面體" data-language-autonym="粵語" data-language-local-name="kantonština" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q188745#sitelinks-wikipedia" title="Editovat mezijazykové odkazy" class="wbc-editpage">Upravit odkazy</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Jmenné prostory"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs 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class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> a všechny stěny tvoří shodné pravidelné <a href="/wiki/Mnoho%C3%BAheln%C3%ADk" title="Mnohoúhelník">mnohoúhelníky</a>. </p><p>Trojrozměrných platónských těles je pět: </p> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Soubor:Tetrahedron.svg" class="mw-file-description" title="Čtyřstěn (animace)"><img alt="Čtyřstěn (animace)" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Tetrahedron.svg/120px-Tetrahedron.svg.png" decoding="async" width="120" height="114" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Tetrahedron.svg/180px-Tetrahedron.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Tetrahedron.svg/240px-Tetrahedron.svg.png 2x" data-file-width="570" data-file-height="540" /></a></span></div> <div class="gallerytext"><a href="/wiki/%C4%8Cty%C5%99st%C4%9Bn" title="Čtyřstěn">Čtyřstěn</a> (<a href="/wiki/Soubor:Tetrahedron.gif" title="Soubor:Tetrahedron.gif">animace</a>)</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Soubor:Hexahedron.svg" class="mw-file-description" title="Krychle (pravidelný šestistěn) (animace)"><img alt="Krychle (pravidelný šestistěn) (animace)" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Hexahedron.svg/108px-Hexahedron.svg.png" decoding="async" width="108" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Hexahedron.svg/162px-Hexahedron.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Hexahedron.svg/216px-Hexahedron.svg.png 2x" data-file-width="540" data-file-height="600" /></a></span></div> <div class="gallerytext"><a href="/wiki/Krychle" title="Krychle">Krychle</a> (pravidelný <a href="/wiki/Krychle" title="Krychle">šestistěn</a>) (<a href="/wiki/Soubor:Hexahedron.gif" title="Soubor:Hexahedron.gif">animace</a>)</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Soubor:Octahedron.svg" class="mw-file-description" title="Osmistěn (animace)"><img alt="Osmistěn (animace)" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Octahedron.svg/120px-Octahedron.svg.png" decoding="async" width="120" height="119" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Octahedron.svg/180px-Octahedron.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/07/Octahedron.svg/240px-Octahedron.svg.png 2x" data-file-width="840" data-file-height="832" /></a></span></div> <div class="gallerytext"><a href="/wiki/Osmist%C4%9Bn" title="Osmistěn">Osmistěn</a> (<a href="/wiki/Soubor:Octahedron.gif" title="Soubor:Octahedron.gif">animace</a>)</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Soubor:Dodecahedron.svg" class="mw-file-description" title="Dvanáctistěn (animace)"><img alt="Dvanáctistěn (animace)" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Dodecahedron.svg/120px-Dodecahedron.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Dodecahedron.svg/180px-Dodecahedron.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Dodecahedron.svg/240px-Dodecahedron.svg.png 2x" data-file-width="300" data-file-height="300" /></a></span></div> <div class="gallerytext"><a href="/wiki/Dvan%C3%A1ctist%C4%9Bn" title="Dvanáctistěn">Dvanáctistěn</a> (<a href="/wiki/Soubor:Dodecahedron.gif" title="Soubor:Dodecahedron.gif">animace</a>)</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Soubor:Icosahedron.svg" class="mw-file-description" title="Dvacetistěn (animace)"><img alt="Dvacetistěn (animace)" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Icosahedron.svg/120px-Icosahedron.svg.png" decoding="async" width="120" height="115" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Icosahedron.svg/180px-Icosahedron.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Icosahedron.svg/240px-Icosahedron.svg.png 2x" data-file-width="512" data-file-height="492" /></a></span></div> <div class="gallerytext"><a href="/wiki/Dvacetist%C4%9Bn" title="Dvacetistěn">Dvacetistěn</a> (<a href="/wiki/Soubor:Icosahedron.gif" title="Soubor:Icosahedron.gif">animace</a>)</div> </li> </ul> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Tabulka_vlastností_platónských_těles"><span id="Tabulka_vlastnost.C3.AD_plat.C3.B3nsk.C3.BDch_t.C4.9Bles"></span>Tabulka vlastností platónských těles</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plat%C3%B3nsk%C3%A9_t%C4%9Bleso&veaction=edit&section=1" title="Editace sekce: Tabulka vlastností platónských těles" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Plat%C3%B3nsk%C3%A9_t%C4%9Bleso&action=edit&section=1" title="Editovat zdrojový kód sekce Tabulka vlastností platónských těles"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Platónských těles existuje v trojrozměrném euklidovském prostoru právě pět a jsou to: </p> <table border="1" cellpadding="9" style="margin:0 auto; text-align:center; border-collapse: collapse;"> <tbody><tr> <th>Název </th> <th>Obrázek </th> <th>Počet stěn </th> <th>Počet hran </th> <th>Počet vrcholů </th> <th>Typ stěny </th> <th>Počet hran u vrcholu </th> <th>Povrch <span style="white-space:nowrap">(hrana délky <b>a</b>)</span> </th> <th>Objem <span style="white-space:nowrap">(hrana délky <b>a</b>)</span> </th></tr> <tr> <td>Pravidelný <a href="/wiki/%C4%8Cty%C5%99st%C4%9Bn" title="Čtyřstěn">čtyřstěn</a> (tetraedr) </td> <td><span typeof="mw:File"><a href="/wiki/Soubor:Tetrahedron.jpg" class="mw-file-description" title="Tetrahedron"><img alt="Tetrahedron" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Tetrahedron.jpg/50px-Tetrahedron.jpg" decoding="async" width="50" height="47" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Tetrahedron.jpg/75px-Tetrahedron.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/Tetrahedron.jpg/100px-Tetrahedron.jpg 2x" data-file-width="643" data-file-height="607" /></a></span><br /> <p>(<a href="/wiki/Soubor:Tetrahedron.gif" title="Soubor:Tetrahedron.gif">animace</a>) </p> </td> <td>4</td> <td>6</td> <td>4</td> <td><a href="/wiki/Troj%C3%BAheln%C3%ADk" title="Trojúhelník">trojúhelník</a></td> <td>3</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {3}}a^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {3}}a^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a13877455b553bd59b9fc996c79e5084a607c67f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.382ex; height:3.009ex;" alt="{\displaystyle {\sqrt {3}}a^{2}}"></span></td> <td><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 {\frac {\sqrt {2}}{12}}a^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>2</mn> </msqrt> <mn>12</mn> </mfrac> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sqrt {2}}{12}}a^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1247bad08baea92baf1fc58b24dec6b625e2eb7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.219ex; height:5.843ex;" alt="{\displaystyle {\frac {\sqrt {2}}{12}}a^{3}}"></span> </td></tr> <tr> <td><a href="/wiki/Krychle" title="Krychle">Krychle</a> (pravidelný šestistěn, hexaedr) </td> <td><span typeof="mw:File"><a href="/wiki/Soubor:Hexahedron.jpg" class="mw-file-description" title="Hexahedron (cube)"><img alt="Hexahedron (cube)" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Hexahedron.jpg/50px-Hexahedron.jpg" decoding="async" width="50" height="56" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Hexahedron.jpg/75px-Hexahedron.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/78/Hexahedron.jpg/100px-Hexahedron.jpg 2x" data-file-width="742" data-file-height="826" /></a></span><br /> <p>(<a href="/wiki/Soubor:Hexahedron.gif" title="Soubor:Hexahedron.gif">animace</a>) </p> </td> <td>6</td> <td>12</td> <td>8</td> <td><a href="/wiki/%C4%8Ctverec" title="Čtverec">čtverec</a></td> <td>3</td> <td><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 6a^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>6</mn> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 6a^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/abd1d7935383caf99e3aece9d1eb41f91a2691f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.447ex; height:2.676ex;" alt="{\displaystyle 6a^{2}}"></span></td> <td><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^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/abd83c98f7301a720f69dd6d4043461e4cc83daa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.284ex; height:2.676ex;" alt="{\displaystyle a^{3}}"></span> </td></tr> <tr> <td>Pravidelný <a href="/wiki/Osmist%C4%9Bn" title="Osmistěn">osmistěn</a> (oktaedr) </td> <td><span typeof="mw:File"><a href="/wiki/Soubor:Octahedron.jpg" class="mw-file-description" title="Octahedron"><img alt="Octahedron" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/Octahedron.jpg/50px-Octahedron.jpg" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/Octahedron.jpg/75px-Octahedron.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/27/Octahedron.jpg/100px-Octahedron.jpg 2x" data-file-width="862" data-file-height="862" /></a></span><br />(<a href="/wiki/Soubor:Octahedron.gif" title="Soubor:Octahedron.gif">animace</a>) </td> <td>8</td> <td>12</td> <td>6</td> <td><a href="/wiki/Troj%C3%BAheln%C3%ADk" title="Trojúhelník">trojúhelník</a></td> <td>4</td> <td><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 2{\sqrt {3}}a^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2{\sqrt {3}}a^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/efae46403e6ea0f604aa065846ec0b942f92c1a4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.545ex; height:3.009ex;" alt="{\displaystyle 2{\sqrt {3}}a^{2}}"></span></td> <td><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 {\frac {\sqrt {2}}{3}}a^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>2</mn> </msqrt> <mn>3</mn> </mfrac> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sqrt {2}}{3}}a^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e7e91e450eba67708ee6664d2a2f02012f2c155" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.219ex; height:5.843ex;" alt="{\displaystyle {\frac {\sqrt {2}}{3}}a^{3}}"></span> </td></tr> <tr> <td>Pravidelný <a href="/wiki/Dvan%C3%A1ctist%C4%9Bn" title="Dvanáctistěn">dvanáctistěn</a> (dodekaedr) </td> <td><span typeof="mw:File"><a href="/wiki/Soubor:Dodecahedron.jpg" class="mw-file-description" title="Dodecahedron"><img alt="Dodecahedron" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Dodecahedron.jpg/50px-Dodecahedron.jpg" decoding="async" width="50" height="49" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Dodecahedron.jpg/75px-Dodecahedron.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Dodecahedron.jpg/100px-Dodecahedron.jpg 2x" data-file-width="847" data-file-height="829" /></a></span><br /> <p>(<a href="/wiki/Soubor:Dodecahedron.gif" title="Soubor:Dodecahedron.gif">animace</a>) </p> </td> <td>12</td> <td>30</td> <td>20</td> <td><a href="/wiki/P%C4%9Bti%C3%BAheln%C3%ADk" title="Pětiúhelník">pětiúhelník</a></td> <td>3</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3{\sqrt {25+10{\sqrt {5}}}}a^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>25</mn> <mo>+</mo> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>5</mn> </msqrt> </mrow> </msqrt> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3{\sqrt {25+10{\sqrt {5}}}}a^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e391b13b2454c6101d2cc4b70b2efa136ab5137d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:16.359ex; height:4.843ex;" alt="{\displaystyle 3{\sqrt {25+10{\sqrt {5}}}}a^{2}}"></span></td> <td><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 {\frac {1}{4}}(15+7{\sqrt {5}})a^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <mn>15</mn> <mo>+</mo> <mn>7</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>5</mn> </msqrt> </mrow> <mo stretchy="false">)</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{4}}(15+7{\sqrt {5}})a^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd4f430f0e1968dfb102c53380a6ee1fd359ccb7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:15.518ex; height:5.176ex;" alt="{\displaystyle {\frac {1}{4}}(15+7{\sqrt {5}})a^{3}}"></span> </td></tr> <tr> <td>Pravidelný <a href="/wiki/Dvacetist%C4%9Bn" title="Dvacetistěn">dvacetistěn</a> (ikosaedr) </td> <td><span typeof="mw:File"><a href="/wiki/Soubor:Icosahedron.jpg" class="mw-file-description" title="Icosahedron"><img alt="Icosahedron" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Icosahedron.jpg/50px-Icosahedron.jpg" decoding="async" width="50" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Icosahedron.jpg/75px-Icosahedron.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Icosahedron.jpg/100px-Icosahedron.jpg 2x" data-file-width="819" data-file-height="791" /></a></span><br /> <p>(<a href="/wiki/Soubor:Icosahedron.gif" title="Soubor:Icosahedron.gif">animace</a>) </p> </td> <td>20</td> <td>30</td> <td>12</td> <td><a href="/wiki/Troj%C3%BAheln%C3%ADk" title="Trojúhelník">trojúhelník</a></td> <td>5</td> <td><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 5{\sqrt {3}}a^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>5</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 5{\sqrt {3}}a^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87a786f1e5125e3bf8d3c5a8cee3f0647b18af35" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.545ex; height:3.009ex;" alt="{\displaystyle 5{\sqrt {3}}a^{2}}"></span></td> <td><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 {\frac {5}{12}}(3+{\sqrt {5}})a^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>5</mn> <mn>12</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <mn>3</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>5</mn> </msqrt> </mrow> <mo stretchy="false">)</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {5}{12}}(3+{\sqrt {5}})a^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a37c793b2f59d8e2852edbb7cb525a6397406215" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.356ex; height:5.176ex;" alt="{\displaystyle {\frac {5}{12}}(3+{\sqrt {5}})a^{3}}"></span> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Dualismus">Dualismus</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plat%C3%B3nsk%C3%A9_t%C4%9Bleso&veaction=edit&section=2" title="Editace sekce: Dualismus" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Plat%C3%B3nsk%C3%A9_t%C4%9Bleso&action=edit&section=2" title="Editovat zdrojový kód sekce Dualismus"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Při pohledu na tabulku je nápadné, že zatím co např. krychle má 8 vrcholů a 6 stěn, u osmistěnu je tomu právě naopak. Proto je krychle <a href="/wiki/Du%C3%A1ln%C3%AD_mnohost%C4%9Bn" title="Duální mnohostěn">duální</a> k osmistěnu. Podobně je dvanáctistěn duální k dvacetistěnu (20 vrcholů, 12 stěn a naopak). Čtyřstěn je duální sám k sobě (má 4 vrcholy a 4 stěny). </p> <div class="mw-heading mw-heading2"><h2 id="Historie">Historie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plat%C3%B3nsk%C3%A9_t%C4%9Bleso&veaction=edit&section=3" title="Editace sekce: Historie" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Plat%C3%B3nsk%C3%A9_t%C4%9Bleso&action=edit&section=3" title="Editovat zdrojový kód sekce Historie"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Platónská tělesa byla známa již ve <a href="/wiki/Starov%C4%9Bk" title="Starověk">starověku</a>. Nazývají se podle <a href="/wiki/%C5%98ecko" title="Řecko">řeckého</a> <a href="/wiki/Filozofie" title="Filozofie">filosofa</a> <a href="/wiki/Plat%C3%B3n" title="Platón">Platóna</a> (427–347 př. n. l.), který <a href="/wiki/Krychle" title="Krychle">krychli</a>, <a href="/wiki/Osmist%C4%9Bn" title="Osmistěn">osmistěn</a>, <a href="/wiki/%C4%8Cty%C5%99st%C4%9Bn" title="Čtyřstěn">čtyřstěn</a> a <a href="/wiki/Dvacetist%C4%9Bn" title="Dvacetistěn">dvacetistěn</a> považoval za představitele čtyř základních živlů: země, vzduch, oheň a voda. <a href="/wiki/Dvan%C3%A1ctist%C4%9Bn" title="Dvanáctistěn">Dvanáctistěn</a> byl představitelem <a href="/wiki/Jsoucno" title="Jsoucno">jsoucna</a> neboli všeho, co existuje. </p><p><a href="/wiki/Eukleid%C3%A9s" title="Eukleidés">Eukleidés</a> sepsal kompletní matematický popis platónských těles ve svých <i>Základech</i>, poslední kniha (kniha XIII) je věnována jejich vlastnostem. Tvrzení 13–17 v knize XIII popisují stavbu čtyřstěnu, krychle, osmistěnu a dvanáctistěnu a dvacetistěnu v uvedeném pořadí. Pro každé Platonské těleso Euklid našel poměr průměru opsané kulové plochy s délkou hrany. Tvrdil, že žádné další pravidelné konvexní mnohostěny neexistují. </p><p><a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Johannes Kepler</a> se pokusil mezi šest tehdy známých <a href="/wiki/Planeta" title="Planeta">planet</a> vložit těchto pět platónských těles. Mezi <a href="/wiki/Merkur_(planeta)" title="Merkur (planeta)">Merkur</a> a <a href="/wiki/Venu%C5%A1e_(planeta)" title="Venuše (planeta)">Venuši</a> dal osmistěn, mezi Venuši a <a href="/wiki/Zem%C4%9B" title="Země">Zemi</a> dvacetistěn, mezi Zemi a <a href="/wiki/Mars_(planeta)" title="Mars (planeta)">Mars</a> dvanáctistěn, mezi Mars a <a href="/wiki/Jupiter_(planeta)" title="Jupiter (planeta)">Jupiter</a> čtyřstěn a mezi Jupiter a <a href="/wiki/Saturn_(planeta)" title="Saturn (planeta)">Saturn</a> krychli. Tato tělesa měla představovat vzdálenosti mezi jednotlivými planetami. </p> <div class="mw-heading mw-heading2"><h2 id="Přírodní_vědy"><span id="P.C5.99.C3.ADrodn.C3.AD_v.C4.9Bdy"></span>Přírodní vědy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plat%C3%B3nsk%C3%A9_t%C4%9Bleso&veaction=edit&section=4" title="Editace sekce: Přírodní vědy" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Plat%C3%B3nsk%C3%A9_t%C4%9Bleso&action=edit&section=4" title="Editovat zdrojový kód sekce Přírodní vědy"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Vzhledem k vysoké symetrii se platónská tělesa objevují běžně v současné <a href="/wiki/Krystalografie" title="Krystalografie">krystalografii</a>, <a href="/w/index.php?title=Krystalochemie&action=edit&redlink=1" class="new" title="Krystalochemie (stránka neexistuje)">krystalochemii</a> a molekulární <a href="/wiki/Fyzika" title="Fyzika">fyzice</a> a <a href="/wiki/Chemie" title="Chemie">chemii</a>. Řada tvarů <a href="/wiki/Krystal" title="Krystal">krystalů</a> s vysokou symetrií krystalové mřížky nabývá forem platónských těles (např. krystaly běžné <a href="/wiki/Halit" title="Halit">kuchyňské soli</a> mají tvar krychle, u <a href="/wiki/Sfalerit" title="Sfalerit">sfaleritu</a> někdy tvar čtyřstěnu apod.). Také symetrické <a href="/wiki/Molekula" title="Molekula">molekuly</a> mají mnohdy tvar těchto těles: <a href="/wiki/Methan" title="Methan">methan</a> má čtyři <a href="/wiki/Atom" title="Atom">atomy</a> <a href="/wiki/Vod%C3%ADk" title="Vodík">vodíku</a> ve vrcholech pravidelného čtyřstěnu s <a href="/wiki/Uhl%C3%ADk" title="Uhlík">uhlíkovým</a> atomem v jeho <a href="/wiki/T%C4%9B%C5%BEi%C5%A1t%C4%9B" title="Těžiště">těžišti</a>, molekula <a href="/wiki/Fluorid_s%C3%ADrov%C3%BD" title="Fluorid sírový">fluoridu sírového</a> má tvar pravidelného osmistěnu atp. </p> <div class="mw-heading mw-heading2"><h2 id="Vyšší_dimenze"><span id="Vy.C5.A1.C5.A1.C3.AD_dimenze"></span>Vyšší dimenze</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plat%C3%B3nsk%C3%A9_t%C4%9Bleso&veaction=edit&section=5" title="Editace sekce: Vyšší dimenze" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Plat%C3%B3nsk%C3%A9_t%C4%9Bleso&action=edit&section=5" title="Editovat zdrojový kód sekce Vyšší dimenze"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pravidelné <a href="/wiki/Mnohost%C4%9Bn" title="Mnohostěn">mnohostěny</a> existují i ve vyšších <a href="/wiki/Dimenze_vektorov%C3%A9ho_prostoru" title="Dimenze vektorového prostoru">dimenzích</a>. </p> <ul><li>Ve čtyřrozměrném prostoru jich je šest: <a href="/wiki/5nadst%C4%9Bn" title="5nadstěn">5nadstěn</a>, <a href="/wiki/Teserakt" title="Teserakt">teserakt</a>, <a href="/wiki/16nadst%C4%9Bn" title="16nadstěn">16nadstěn</a>, <a href="/wiki/24nadst%C4%9Bn" title="24nadstěn">24nadstěn</a>, <a href="/wiki/120nadst%C4%9Bn" title="120nadstěn">120nadstěn</a>, <a href="/wiki/600nadst%C4%9Bn" title="600nadstěn">600nadstěn</a>.</li> <li>V prostorech dimenze vyšší než čtyři existují vždy právě tři pravidelné mnohostěny: zobecnění <a href="/wiki/%C4%8Cty%C5%99st%C4%9Bn" title="Čtyřstěn">čtyřstěnu</a>, zobecnění <a href="/wiki/Krychle" title="Krychle">krychle</a> a její duální těleso – zobecnění <a href="/wiki/Osmist%C4%9Bn" title="Osmistěn">osmistěnu</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Odkazy">Odkazy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plat%C3%B3nsk%C3%A9_t%C4%9Bleso&veaction=edit&section=6" title="Editace sekce: Odkazy" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Plat%C3%B3nsk%C3%A9_t%C4%9Bleso&action=edit&section=6" title="Editovat zdrojový kód sekce Odkazy"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Poznámky"><span id="Pozn.C3.A1mky"></span>Poznámky</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plat%C3%B3nsk%C3%A9_t%C4%9Bleso&veaction=edit&section=7" title="Editace sekce: Poznámky" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Plat%C3%B3nsk%C3%A9_t%C4%9Bleso&action=edit&section=7" title="Editovat zdrojový kód sekce Poznámky"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Ekvivalentní definice říká, že v každém vrcholu se stýká stejný počet stěn.</span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Reference">Reference</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plat%C3%B3nsk%C3%A9_t%C4%9Bleso&veaction=edit&section=8" title="Editace sekce: Reference" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Plat%C3%B3nsk%C3%A9_t%C4%9Bleso&action=edit&section=8" title="Editovat zdrojový kód sekce Reference"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="plainlinks"><i>V tomto článku byl použit <a href="/wiki/Wikipedie:WikiProjekt_P%C5%99eklad/Rady" title="Wikipedie:WikiProjekt Překlad/Rady">překlad</a> textu z článku <a class="external text" href="https://en.wikipedia.org/wiki/Platonic_solid?oldid=480695824"><span class="cizojazycne" lang="en" title="angličtina">Platonic solid</span></a> na anglické Wikipedii.</i></span> </p> <div class="mw-heading mw-heading3"><h3 id="Související_články"><span id="Souvisej.C3.ADc.C3.AD_.C4.8Dl.C3.A1nky"></span>Související články</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plat%C3%B3nsk%C3%A9_t%C4%9Bleso&veaction=edit&section=9" title="Editace sekce: Související články" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Plat%C3%B3nsk%C3%A9_t%C4%9Bleso&action=edit&section=9" title="Editovat zdrojový kód sekce Související články"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Polopravideln%C3%BD_mnohost%C4%9Bn" title="Polopravidelný mnohostěn">Polopravidelná tělesa</a></li> <li><a href="/wiki/%C4%8Cty%C5%99rozm%C4%9Brn%C3%A1_plat%C3%B3nsk%C3%A1_t%C4%9Blesa" title="Čtyřrozměrná platónská tělesa">Čtyřrozměrná platónská tělesa</a></li> <li><a href="/w/index.php?title=N-rozm%C4%9Brn%C3%A1_plat%C3%B3nsk%C3%A1_t%C4%9Blesa&action=edit&redlink=1" class="new" title="N-rozměrná platónská tělesa (stránka neexistuje)">n-rozměrná platónská tělesa</a></li> <li><a href="/wiki/Archim%C3%A9dovsk%C3%A9_t%C4%9Bleso" title="Archimédovské těleso">Archimédovské těleso</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Externí_odkazy"><span id="Extern.C3.AD_odkazy"></span>Externí odkazy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plat%C3%B3nsk%C3%A9_t%C4%9Bleso&veaction=edit&section=10" title="Editace sekce: Externí odkazy" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Plat%C3%B3nsk%C3%A9_t%C4%9Bleso&action=edit&section=10" title="Editovat zdrojový kód sekce Externí odkazy"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="wd"><span class="sisterproject sisterproject-commons"><span class="sisterproject_image"><span typeof="mw:File"><a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons"><img alt="Logo Wikimedia Commons" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></span> <span class="sisterproject_text">Obrázky, zvuky či videa k tématu <span class="sisterproject_text_target"><a href="https://commons.wikimedia.org/wiki/Category:Platonic_solids" class="extiw" title="c:Category:Platonic solids">platónské těleso</a></span> na <a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons">Wikimedia Commons</a></span></span></span><i> </i></li> <li><a rel="nofollow" class="external free" href="http://www.darius.cz/ag_nikola/cl_dvanacti.html">http://www.darius.cz/ag_nikola/cl_dvanacti.html</a></li> <li><a rel="nofollow" class="external free" href="http://telesa.wz.cz">http://telesa.wz.cz</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150610215933/http://telesa.wz.cz/">Archivováno</a> 10. 6. 2015 na <a href="/wiki/Internet_Archive" title="Internet Archive">Wayback Machine</a>. (databáze těles)</li></ul> <style data-mw-deduplicate="TemplateStyles:r23078045">.mw-parser-output .navbox2{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox2 .navbox2{margin-top:0}.mw-parser-output .navbox2+.navbox2{margin-top:-1px}.mw-parser-output .navbox2-inner,.mw-parser-output .navbox2-subgroup{width:100%}.mw-parser-output .navbox2-group,.mw-parser-output .navbox2-title,.mw-parser-output .navbox2-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output th.navbox2-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox2,.mw-parser-output .navbox2-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox2-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output tr+tr>.navbox2-abovebelow,.mw-parser-output tr+tr>.navbox2-group,.mw-parser-output tr+tr>.navbox2-image,.mw-parser-output tr+tr>.navbox2-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox2 th,.mw-parser-output .navbox2-title{background-color:#e0e0e0}.mw-parser-output .navbox2-abovebelow,.mw-parser-output th.navbox2-group,.mw-parser-output .navbox2-subgroup .navbox2-title{background-color:#e7e7e7}.mw-parser-output .navbox2-subgroup .navbox2-title{font-size:88%}.mw-parser-output .navbox2-subgroup .navbox2-group,.mw-parser-output .navbox2-subgroup .navbox2-abovebelow{background-color:#f0f0f0}.mw-parser-output .navbox2-even{background-color:#f7f7f7}.mw-parser-output .navbox2-odd{background-color:transparent}.mw-parser-output .navbox2 .hlist td dl,.mw-parser-output .navbox2 .hlist td ol,.mw-parser-output .navbox2 .hlist td ul,.mw-parser-output .navbox2 td.hlist dl,.mw-parser-output .navbox2 td.hlist ol,.mw-parser-output .navbox2 td.hlist ul{padding:0.125em 0}</style><div role="navigation" class="navbox2" aria-labelledby="Autoritní_data_frameless_&#124;text-top_&#124;10px_&#124;alt=Editovat_na_Wikidatech_&#124;link=https&#58;//www.wikidata.org/wiki/Q188745#identifiers&#124;Editovat_na_Wikidatech" style="padding:2px"><table class="nowraplinks hlist navbox2-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="Autoritní_data_frameless_&#124;text-top_&#124;10px_&#124;alt=Editovat_na_Wikidatech_&#124;link=https&#58;//www.wikidata.org/wiki/Q188745#identifiers&#124;Editovat_na_Wikidatech" scope="row" class="navbox2-group" style="width:1%"><a href="/wiki/Autoritn%C3%AD_kontrola" title="Autoritní kontrola">Autoritní data</a> <span class="mw-valign-text-top" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q188745#identifiers" title="Editovat na Wikidatech"><img alt="Editovat na Wikidatech" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></th><td class="navbox2-list navbox2-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Gemeinsame_Normdatei" title="Gemeinsame Normdatei">GND</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4046302-3">4046302-3</a></span></span></li></ul> </div></td></tr></tbody></table></div> <style data-mw-deduplicate="TemplateStyles:r16915398">.mw-parser-output div/**/#portallinks a{font-weight:bold}</style><div id="portallinks" class="catlinks"><a href="/wiki/Port%C3%A1l:Obsah" title="Portál:Obsah">Portály</a>: <a href="/wiki/Port%C3%A1l:Matematika" title="Portál:Matematika">Matematika</a> </div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; 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