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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">Início</div> </a> </li> <li id="toc-Elementos" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Elementos"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Elementos</span> </div> </a> <ul id="toc-Elementos-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Área_e_volume" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Área_e_volume"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Área e volume</span> </div> </a> <ul id="toc-Área_e_volume-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Planificação" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Planificação"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Planificação</span> </div> </a> <ul id="toc-Planificação-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dual" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Dual"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Dual</span> </div> </a> <ul id="toc-Dual-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Icosaedro_na_Natureza" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Icosaedro_na_Natureza"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Icosaedro na Natureza</span> </div> </a> <ul id="toc-Icosaedro_na_Natureza-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Uso" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Uso"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Uso</span> </div> </a> <button aria-controls="toc-Uso-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>Alternar a subsecção Uso</span> </button> <ul id="toc-Uso-sublist" class="vector-toc-list"> <li id="toc-Em_Jogos" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Em_Jogos"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Em Jogos</span> </div> </a> <ul id="toc-Em_Jogos-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Na_Tensegridade" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Na_Tensegridade"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Na Tensegridade</span> </div> </a> <ul id="toc-Na_Tensegridade-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Ver_também" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ver_também"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Ver também</span> </div> </a> <ul id="toc-Ver_também-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referências" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referências"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Referências</span> </div> </a> <ul id="toc-Referências-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ligações_externas" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ligações_externas"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Ligações externas</span> </div> </a> <ul id="toc-Ligações_externas-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="Conteúdo" 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="Alternar o índice" > <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">Alternar o índice</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">Icosaedro</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="Ir para um artigo noutra língua. Disponível em 49 línguas" > <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-49" 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">49 línguas</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/Ikosa%C3%ABder" title="Ikosaëder — africanês" lang="af" hreflang="af" data-title="Ikosaëder" data-language-autonym="Afrikaans" data-language-local-name="africanês" 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/%D8%B9%D8%B4%D8%B1%D9%88%D9%86%D9%8A_%D8%B3%D8%B7%D9%88%D8%AD" title="عشروني سطوح — árabe" lang="ar" hreflang="ar" data-title="عشروني سطوح" data-language-autonym="العربية" data-language-local-name="árabe" 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/%C4%B0kosaedr" title="İkosaedr — azerbaijano" lang="az" hreflang="az" data-title="İkosaedr" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaijano" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%98%D0%BA%D0%BE%D1%81%D0%B0%D0%B5%D0%B4%D1%8A%D1%80" title="Икосаедър — búlgaro" lang="bg" hreflang="bg" data-title="Икосаедър" data-language-autonym="Български" data-language-local-name="búlgaro" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Icosaedre" title="Icosaedre — catalão" lang="ca" hreflang="ca" data-title="Icosaedre" data-language-autonym="Català" data-language-local-name="catalão" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Dvacetist%C4%9Bn" title="Dvacetistěn — checo" lang="cs" hreflang="cs" data-title="Dvacetistěn" data-language-autonym="Čeština" data-language-local-name="checo" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Ikosaeder" title="Ikosaeder — dinamarquês" lang="da" hreflang="da" data-title="Ikosaeder" data-language-autonym="Dansk" data-language-local-name="dinamarquês" 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/Ikosaeder" title="Ikosaeder — alemão" lang="de" hreflang="de" data-title="Ikosaeder" data-language-autonym="Deutsch" data-language-local-name="alemão" 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%95%CE%B9%CE%BA%CE%BF%CF%83%CE%AC%CE%B5%CE%B4%CF%81%CE%BF" title="Εικοσάεδρο — grego" lang="el" hreflang="el" data-title="Εικοσάεδρο" data-language-autonym="Ελληνικά" data-language-local-name="grego" 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/Icosahedron" title="Icosahedron — inglês" lang="en" hreflang="en" data-title="Icosahedron" data-language-autonym="English" data-language-local-name="inglês" 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/Dudekedro" title="Dudekedro — esperanto" lang="eo" hreflang="eo" data-title="Dudekedro" 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/Icosaedro" title="Icosaedro — espanhol" lang="es" hreflang="es" data-title="Icosaedro" data-language-autonym="Español" data-language-local-name="espanhol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Ikosaeeder" title="Ikosaeeder — estónio" lang="et" hreflang="et" data-title="Ikosaeeder" data-language-autonym="Eesti" data-language-local-name="estónio" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Ikosaedro" title="Ikosaedro — basco" lang="eu" hreflang="eu" data-title="Ikosaedro" data-language-autonym="Euskara" data-language-local-name="basco" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A8%DB%8C%D8%B3%D8%AA%E2%80%8C%D9%88%D8%AC%D9%87%DB%8C" title="بیست‌وجهی — persa" lang="fa" hreflang="fa" data-title="بیست‌وجهی" data-language-autonym="فارسی" data-language-local-name="persa" 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/Ikosaedri" title="Ikosaedri — finlandês" lang="fi" hreflang="fi" data-title="Ikosaedri" data-language-autonym="Suomi" data-language-local-name="finlandês" 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/Icosa%C3%A8dre" title="Icosaèdre — francês" lang="fr" hreflang="fr" data-title="Icosaèdre" data-language-autonym="Français" data-language-local-name="francês" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Icosaedro" title="Icosaedro — galego" lang="gl" hreflang="gl" data-title="Icosaedro" data-language-autonym="Galego" data-language-local-name="galego" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he badge-Q70894304 mw-list-item" title=""><a href="https://he.wikipedia.org/wiki/%D7%A2%D7%A9%D7%A8%D7%99%D7%9E%D7%95%D7%9F" title="עשרימון — hebraico" lang="he" hreflang="he" data-title="עשרימון" data-language-autonym="עברית" data-language-local-name="hebraico" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Ikosaedar" title="Ikosaedar — croata" lang="hr" hreflang="hr" data-title="Ikosaedar" data-language-autonym="Hrvatski" data-language-local-name="croata" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Ikoza%C3%A9der" title="Ikozaéder — húngaro" lang="hu" hreflang="hu" data-title="Ikozaéder" data-language-autonym="Magyar" data-language-local-name="húngaro" 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/%D5%94%D5%BD%D5%A1%D5%B6%D5%A1%D5%B6%D5%AB%D5%BD%D5%BF" title="Քսանանիստ — arménio" lang="hy" hreflang="hy" data-title="Քսանանիստ" data-language-autonym="Հայերեն" data-language-local-name="arménio" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Ikosahedron" title="Ikosahedron — indonésio" lang="id" hreflang="id" data-title="Ikosahedron" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonésio" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Ikosaedro" title="Ikosaedro — ido" lang="io" hreflang="io" data-title="Ikosaedro" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Icosaedro" title="Icosaedro — italiano" lang="it" hreflang="it" data-title="Icosaedro" data-language-autonym="Italiano" data-language-local-name="italiano" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%BA%8C%E5%8D%81%E9%9D%A2%E4%BD%93" title="二十面体 — japonês" lang="ja" hreflang="ja" data-title="二十面体" data-language-autonym="日本語" data-language-local-name="japonês" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%98%D0%BA%D0%BE%D1%81%D0%B0%D1%8D%D0%B4%D1%80" title="Икосаэдр — cazaque" lang="kk" hreflang="kk" data-title="Икосаэдр" data-language-autonym="Қазақша" data-language-local-name="cazaque" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9D%B4%EC%8B%AD%EB%A9%B4%EC%B2%B4" title="이십면체 — coreano" lang="ko" hreflang="ko" data-title="이십면체" data-language-autonym="한국어" data-language-local-name="coreano" 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/Icosahedron" title="Icosahedron — latim" lang="la" hreflang="la" data-title="Icosahedron" data-language-autonym="Latina" data-language-local-name="latim" 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/Ikosaedras" title="Ikosaedras — lituano" lang="lt" hreflang="lt" data-title="Ikosaedras" data-language-autonym="Lietuvių" data-language-local-name="lituano" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Ikosaedrs" title="Ikosaedrs — letão" lang="lv" hreflang="lv" data-title="Ikosaedrs" data-language-autonym="Latviešu" data-language-local-name="letão" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-nl badge-Q70894304 mw-list-item" title=""><a href="https://nl.wikipedia.org/wiki/Icosa%C3%ABder" title="Icosaëder — neerlandês" lang="nl" hreflang="nl" data-title="Icosaëder" data-language-autonym="Nederlands" data-language-local-name="neerlandês" 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/Ikosaeder" title="Ikosaeder — norueguês nynorsk" lang="nn" hreflang="nn" data-title="Ikosaeder" data-language-autonym="Norsk nynorsk" data-language-local-name="norueguês 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/Ikosaeder" title="Ikosaeder — norueguês bokmål" lang="nb" hreflang="nb" data-title="Ikosaeder" data-language-autonym="Norsk bokmål" data-language-local-name="norueguês bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Icosaedru" title="Icosaedru — romeno" lang="ro" hreflang="ro" data-title="Icosaedru" data-language-autonym="Română" data-language-local-name="romeno" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-rsk mw-list-item"><a href="https://rsk.wikipedia.org/wiki/%D0%98%D0%BA%D0%BE%D1%81%D0%B0%D0%B5%D0%B4%D0%B5%D1%80" title="Икосаедер — Pannonian Rusyn" lang="rsk" hreflang="rsk" data-title="Икосаедер" data-language-autonym="Руски" data-language-local-name="Pannonian Rusyn" class="interlanguage-link-target"><span>Руски</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%98%D0%BA%D0%BE%D1%81%D0%B0%D1%8D%D0%B4%D1%80" title="Икосаэдр — russo" lang="ru" hreflang="ru" data-title="Икосаэдр" data-language-autonym="Русский" data-language-local-name="russo" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Icosaedru" title="Icosaedru — siciliano" lang="scn" hreflang="scn" data-title="Icosaedru" data-language-autonym="Sicilianu" data-language-local-name="siciliano" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Ikosaedar" title="Ikosaedar — servo-croata" lang="sh" hreflang="sh" data-title="Ikosaedar" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="servo-croata" 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/Icosahedron" title="Icosahedron — Simple English" lang="en-simple" hreflang="en-simple" data-title="Icosahedron" 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/Dvadsa%C5%A5sten" title="Dvadsaťsten — eslovaco" lang="sk" hreflang="sk" data-title="Dvadsaťsten" data-language-autonym="Slovenčina" data-language-local-name="eslovaco" 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/Ikozaeder" title="Ikozaeder — esloveno" lang="sl" hreflang="sl" data-title="Ikozaeder" data-language-autonym="Slovenščina" data-language-local-name="esloveno" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Ikosaeder" title="Ikosaeder — sueco" lang="sv" hreflang="sv" data-title="Ikosaeder" data-language-autonym="Svenska" data-language-local-name="sueco" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%97%E0%B8%A3%E0%B8%87%E0%B8%A2%E0%B8%B5%E0%B9%88%E0%B8%AA%E0%B8%B4%E0%B8%9A%E0%B8%AB%E0%B8%99%E0%B9%89%E0%B8%B2" title="ทรงยี่สิบหน้า — tailandês" lang="th" hreflang="th" data-title="ทรงยี่สิบหน้า" data-language-autonym="ไทย" data-language-local-name="tailandês" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%98%D0%BA%D0%BE%D1%81%D0%B0%D1%8D%D0%B4%D1%80" title="Икосаэдр — tatar" lang="tt" hreflang="tt" data-title="Икосаэдр" data-language-autonym="Татарча / tatarça" data-language-local-name="tatar" 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%86%D0%BA%D0%BE%D1%81%D0%B0%D0%B5%D0%B4%D1%80" title="Ікосаедр — ucraniano" lang="uk" hreflang="uk" data-title="Ікосаедр" data-language-autonym="Українська" data-language-local-name="ucraniano" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Ikosaedr" title="Ikosaedr — usbeque" lang="uz" hreflang="uz" data-title="Ikosaedr" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="usbeque" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Nh%E1%BB%8B_th%E1%BA%ADp_di%E1%BB%87n" title="Nhị thập diện — vietnamita" lang="vi" hreflang="vi" data-title="Nhị thập diện" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamita" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%BA%8C%E5%8D%81%E9%9D%A2%E4%BD%93" title="二十面体 — chinês" lang="zh" hreflang="zh" data-title="二十面体" 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vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Aspeto</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mover para a barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ocultar</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Origem: Wikipédia, a enciclopédia livre.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="pt" dir="ltr"><figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:Icosahedron.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Icosahedron.jpg/270px-Icosahedron.jpg" decoding="async" width="270" height="261" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Icosahedron.jpg/405px-Icosahedron.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Icosahedron.jpg/540px-Icosahedron.jpg 2x" data-file-width="819" data-file-height="791" /></a><figcaption>Icosaedro</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:Icosaedro_plat%C3%B4nico.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Icosaedro_plat%C3%B4nico.jpg/270px-Icosaedro_plat%C3%B4nico.jpg" decoding="async" width="270" height="127" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Icosaedro_plat%C3%B4nico.jpg/405px-Icosaedro_plat%C3%B4nico.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Icosaedro_plat%C3%B4nico.jpg/540px-Icosaedro_plat%C3%B4nico.jpg 2x" data-file-width="19141" data-file-height="9034" /></a><figcaption>Rotação total de um icosaedro - <a href="/wiki/Matemateca_IME-USP" class="mw-redirect" title="Matemateca IME-USP">Matemateca IME-USP</a></figcaption></figure> <div class="noprint" style="clear: right; border: solid #aaa 1px; margin: 0 0 1em 1em; font-size: 90%; background: var(--background-color-neutral-subtle, #f9f9f9); color: inherit; width: 238px; padding: 5px; spacing: 2px; text-align: center; float: right;"> <div style="float: left; vertical-align:middle;"><figure class="mw-halign-none" typeof="mw:File"><a href="/wiki/Ficheiro:Commons-logo.svg" class="mw-file-description" title="Commons"><img alt="Commons" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/22px-Commons-logo.svg.png" decoding="async" width="22" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/33px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/44px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a><figcaption>Commons</figcaption></figure></div> <div style="margin-left: 30px; line-height:normal; vertical-align:middle;">O <a href="https://commons.wikimedia.org/wiki/P%C3%A1gina_principal" class="extiw" title="commons:Página principal">Commons</a> possui imagens e outros ficheiros sobre <b><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/w/index.php?title=Icosahedron&uselang=pt">Icosaedro</a></span></b></div> </div> <p>Um <b>icosaedro</b> é um <a href="/wiki/Poliedro" title="Poliedro">poliedro</a> convexo de 20 faces. Um icosaedro regular é constituido por 20 triângulos equiláteros e é um dos <a href="/wiki/S%C3%B3lidos_plat%C3%B3nicos" class="mw-redirect" title="Sólidos platónicos">sólidos platónicos</a>. O icosaedro também pode ser chamado <i>tetraedro snub,</i> pois a <a href="/wiki/Snubifica%C3%A7%C3%A3o" title="Snubificação">snubificação</a> de um <a href="/wiki/Tetraedro" title="Tetraedro">tetraedro</a> regular dá um icosaedro regular. O estudo das figuras geométricas sólidas perfeitas, como o Icosaedro, é de tamanha importância para a matemática, mais especificamente para a <a href="/wiki/Geometria_espacial" title="Geometria espacial">geometria espacial</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Elementos">Elementos</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Icosaedro&veaction=edit&section=1" title="Editar secção: Elementos" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Icosaedro&action=edit&section=1" title="Editar código-fonte da secção: Elementos"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As 20 faces do icosaedro são triangulares. Ao todo são 30 arestas e 12 vértices. Cada vértice é o encontro de 5 arestas. </p><p>Para calcularmos o número de diagonais no icosaedro, tomemos qualquer um dos 12 vértices e podemos ligá-lo a 6 outros vértices (exclui o vértice escolhido e 5 vértices que são ligados ao vértice escolhido por uma aresta). Por este modo, contamos duas vezes cada diagonal, assim, dividimos por 2 ao final. Logo, o número de diagonais é 36. </p><p>Matematicamente, o número de diagonais <b>D</b> do icosaedro é: </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 D={12\cdot 6 \over 2}=36}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>12</mn> <mo>⋅</mo> <mn>6</mn> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mn>36</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D={12\cdot 6 \over 2}=36}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fade1c0df4785d466bd99e6d889ae8ff27fbf567" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.449ex; height:5.176ex;" alt="{\displaystyle D={12\cdot 6 \over 2}=36}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Área_e_volume"><span id=".C3.81rea_e_volume"></span>Área e volume</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Icosaedro&veaction=edit&section=2" title="Editar secção: Área e volume" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Icosaedro&action=edit&section=2" title="Editar código-fonte da secção: Área e volume"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A área da superfície <i>A</i>, e o <a href="/wiki/Volume" title="Volume">volume</a> <i>V</i> de um icosaedro regular, com o comprimento do lado de cada face <i>a</i> são: </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=5{\sqrt {3}}l^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mn>5</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> <msup> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=5{\sqrt {3}}l^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/553b0ce87793a38bc74ac90f1ac850a685e2b62c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.85ex; height:3.009ex;" alt="{\displaystyle A=5{\sqrt {3}}l^{2}}"></span></dd> <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={\begin{matrix}{5 \over 12}\end{matrix}}(3+{\sqrt {5}})l^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>5</mn> <mn>12</mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </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>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V={\begin{matrix}{5 \over 12}\end{matrix}}(3+{\sqrt {5}})l^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8027681cd634ea3d017feaea8b1b44688f91670b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.986ex; margin-bottom: -0.185ex; width:18.775ex; height:3.509ex;" alt="{\displaystyle V={\begin{matrix}{5 \over 12}\end{matrix}}(3+{\sqrt {5}})l^{3}}"></span></dd></dl> <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 l}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/829091f745070b9eb97a80244129025440a1cfac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.693ex; height:2.176ex;" alt="{\displaystyle l}"></span> = valor dos lados</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Planificação"><span id="Planifica.C3.A7.C3.A3o"></span>Planificação</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Icosaedro&veaction=edit&section=3" title="Editar secção: Planificação" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Icosaedro&action=edit&section=3" title="Editar código-fonte da secção: Planificação"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Planifica%C3%A7%C3%A3o_de_um_poliedro" title="Planificação de um poliedro">Planificação</a> de um icosaedro </p><p><span typeof="mw:File"><a href="/wiki/Ficheiro:Icosahedron_flat.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Icosahedron_flat.svg/180px-Icosahedron_flat.svg.png" decoding="async" width="180" height="92" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Icosahedron_flat.svg/270px-Icosahedron_flat.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Icosahedron_flat.svg/360px-Icosahedron_flat.svg.png 2x" data-file-width="236" data-file-height="120" /></a></span> </p> <div class="mw-heading mw-heading2"><h2 id="Dual">Dual</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Icosaedro&veaction=edit&section=4" title="Editar secção: Dual" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Icosaedro&action=edit&section=4" title="Editar código-fonte da secção: Dual"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>O <a href="/wiki/Poliedro_dual" title="Poliedro dual">poliedro dual</a> do icosaedro é o <a href="/wiki/Dodecaedro" title="Dodecaedro">dodecaedro</a> </p><p><span typeof="mw:File"><a href="/wiki/Ficheiro:Dualicosaedre.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Dualicosaedre.png/200px-Dualicosaedre.png" decoding="async" width="200" height="213" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Dualicosaedre.png/300px-Dualicosaedre.png 1.5x, //upload.wikimedia.org/wikipedia/commons/e/eb/Dualicosaedre.png 2x" data-file-width="310" data-file-height="330" /></a></span> </p> <div class="mw-heading mw-heading2"><h2 id="Icosaedro_na_Natureza">Icosaedro na Natureza</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Icosaedro&veaction=edit&section=5" title="Editar secção: Icosaedro na Natureza" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Icosaedro&action=edit&section=5" title="Editar código-fonte da secção: Icosaedro na Natureza"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:Circogoniaicosahedra_ekw.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/0/02/Circogoniaicosahedra_ekw.jpg" decoding="async" width="157" height="175" class="mw-file-element" data-file-width="157" data-file-height="175" /></a><figcaption>Circogonia icosahedra</figcaption></figure> <p>Muitos <a href="/wiki/V%C3%ADrus" title="Vírus">vírus</a>, como por exemplo o vírus do <a href="/wiki/Herpes" title="Herpes">Herpes</a> e <a href="/wiki/Protista" title="Protista">Protistas</a> radiolários como a <i>Circogonia icosahedra</i>, têm a forma de um Icosaedro. </p><p><br /> </p> <div class="mw-heading mw-heading2"><h2 id="Uso">Uso</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Icosaedro&veaction=edit&section=6" title="Editar secção: Uso" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Icosaedro&action=edit&section=6" title="Editar código-fonte da secção: Uso"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:20-sided_dice_250.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/9/97/20-sided_dice_250.jpg" decoding="async" width="162" height="153" class="mw-file-element" data-file-width="162" data-file-height="153" /></a><figcaption><a href="/wiki/Dado" class="mw-disambig" title="Dado">Dado</a> de 20 lados</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Em_Jogos">Em Jogos</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Icosaedro&veaction=edit&section=7" title="Editar secção: Em Jogos" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Icosaedro&action=edit&section=7" title="Editar código-fonte da secção: Em Jogos"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Icosaedros são usados como <a href="/wiki/Dado" class="mw-disambig" title="Dado">dados</a> de 20 lados desde a <a href="/wiki/Antiguidade" class="mw-redirect" title="Antiguidade">Antiguidade</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span>[</span>1<span>]</span></a></sup> Em vários <a href="/wiki/RPG_(jogo)" class="mw-redirect" title="RPG (jogo)">jogos de RPG</a>, como <a href="/wiki/Dungeons_%26_Dragons" title="Dungeons & Dragons">Dungeons & Dragons</a>, o dado de vinte faces (mais conhecido como D20) é comumente usado para determinar o sucesso ou o fracasso de uma ação. Este dado é na forma de um icosaedro (veja <a href="/wiki/Sistema_d20" title="Sistema d20">sistema d20</a>). No jogo de cartas <a href="/wiki/Magic:_The_Gathering" title="Magic: The Gathering">Magic: The Gathering</a>, o dado de 20 lados é comumente utilizado para marcar os pontos de vida dos jogadores, sendo eles fornecidos em vários kits pela própria empresa que fabrica as cartas, a <a href="/wiki/Wizards_of_the_Coast" title="Wizards of the Coast">Wizards of the Coast</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Na_Tensegridade">Na Tensegridade</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Icosaedro&veaction=edit&section=8" title="Editar secção: Na Tensegridade" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Icosaedro&action=edit&section=8" title="Editar código-fonte da secção: Na Tensegridade"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>O <a href="/wiki/Octaedro" title="Octaedro">octaedro</a> tem sido amplamente estudado no campo da <a href="/wiki/Tensegridade" title="Tensegridade">tensegridade</a>. Devido à sua simetria esférica e alta relação resistência-peso, a forma tornou-se um bom candidato para estruturas espaciais de tensegridade implantáveis, como o SuperBALL da NASA.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span>[</span>2<span>]</span></a></sup> O robô é composto por hastes, cabos e atuadores de diferentes escalas e está atualmente em desenvolvimento entre o Grupo de Robótica Inteligente do Centro de Pesquisa Ames da NASA e o Laboratório de Tensegridade Robótica Dinâmica (DTRL). Sua configuração não implantada é altamente compacta, tornando-o ideal para se encaixar nas restrições de espaço das carenagens de foguetes.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span>[</span>3<span>]</span></a></sup> </p><p>O icosaedro em tensegridade é composto por seis barras e vinte e quatro cabos que conectam doze nós. Um estado de autotensão está presente na combinação alcançada por meio do uso de morfogênese celular.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span>[</span>4<span>]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Ver_também"><span id="Ver_tamb.C3.A9m"></span>Ver também</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Icosaedro&veaction=edit&section=9" title="Editar secção: Ver também" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Icosaedro&action=edit&section=9" title="Editar código-fonte da secção: Ver também"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Icosaedro_truncado" title="Icosaedro truncado">Icosaedro truncado</a></li> <li><a href="/wiki/Icosaedro_triakis" title="Icosaedro triakis">Icosaedro triakis</a></li></ul> <h2 id="Referências" style="cursor: help;" title="Esta seção foi configurada para não ser editável diretamente. Edite a página toda ou a seção anterior em vez disso."><span id="Refer.C3.AAncias"></span>Referências</h2> <div class="reflist" style="list-style-type: decimal;"><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">Cromwell, Peter R. "Polyhedra" (1997) p. 327.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><cite class="citation journal">Sabelhaus, Andrew P.; Bruce, Jonathan; Caluwaerts, Ken; Chen, Yangxin; Lu, Dizhou; Liu, Yuejia; Agogino, Adrian K.; SunSpiral, Vytas; Agogino, Alice M. (15 de julho de 2014). <a rel="nofollow" class="external text" href="https://ntrs.nasa.gov/citations/20140011157">«Hardware Design and Testing of SUPERball, A Modular Tensegrity Robot»</a> (em inglês)</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fpt.wikipedia.org%3AIcosaedro&rft.atitle=Hardware+Design+and+Testing+of+SUPERball%2C+A+Modular+Tensegrity+Robot&rft.au=Agogino%2C+Adrian+K.&rft.au=Agogino%2C+Alice+M.&rft.au=Bruce%2C+Jonathan&rft.au=Caluwaerts%2C+Ken&rft.au=Chen%2C+Yangxin&rft.au=Liu%2C+Yuejia&rft.au=Lu%2C+Dizhou&rft.au=SunSpiral%2C+Vytas&rft.aufirst=Andrew+P.&rft.aulast=Sabelhaus&rft.date=2014-07-15&rft.genre=article&rft_id=https%3A%2F%2Fntrs.nasa.gov%2Fcitations%2F20140011157&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="https://spectrum.ieee.org/nasa-super-ball-bot">«NASA's Super Ball Bot Could Be the Best Design for Planetary Exploration»</a>. <i>IEEE Spectrum</i> (em inglês). 2 de março de 2015<span class="reference-accessdate">. Consultado em 22 de dezembro de 2022</span></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fpt.wikipedia.org%3AIcosaedro&rft.atitle=NASA%27s+Super+Ball+Bot+Could+Be+the+Best+Design+for+Planetary+Exploration&rft.date=2015-03-02&rft.genre=unknown&rft.jtitle=IEEE+Spectrum&rft_id=https%3A%2F%2Fspectrum.ieee.org%2Fnasa-super-ball-bot&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"><cite class="citation journal">Aloui, Omar; Flores, Jessica; Orden, David; Rhode-Barbarigos, Landolf (1 de abril de 2019). <a rel="nofollow" class="external text" href="https://www.sciencedirect.com/science/article/pii/S0045782518305814">«Cellular morphogenesis of three-dimensional tensegrity structures»</a>. <i>Computer Methods in Applied Mechanics and Engineering</i> (em inglês). <b>346</b>: 85–108. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>:<a rel="nofollow" class="external text" href="http://ui.adsabs.harvard.edu/abs/2019CMAME.346...85A">2019CMAME.346...85A</a>. <a href="/wiki/International_Standard_Serial_Number" title="International Standard Serial Number">ISSN</a> <a rel="nofollow" class="external text" href="//www.worldcat.org/issn/0045-7825">0045-7825</a>. <a href="/wiki/ArXiv" title="ArXiv">arXiv</a>:<span class="plainlinks"><a rel="nofollow" class="external text" href="//arxiv.org/abs/1902.09953">1902.09953</a><span style="margin-left:0.1em"><span typeof="mw:File"><span title="Acessível livremente"><img alt="Acessível livremente" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" /></span></span></span></span>. <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1016%2Fj.cma.2018.10.048">10.1016/j.cma.2018.10.048</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fpt.wikipedia.org%3AIcosaedro&rft.atitle=Cellular+morphogenesis+of+three-dimensional+tensegrity+structures&rft.au=Flores%2C+Jessica&rft.au=Orden%2C+David&rft.au=Rhode-Barbarigos%2C+Landolf&rft.aufirst=Omar&rft.aulast=Aloui&rft.date=2019-04-01&rft.genre=article&rft.issn=0045-7825&rft.jtitle=Computer+Methods+in+Applied+Mechanics+and+Engineering&rft.pages=85-108&rft.volume=346&rft_id=https%3A%2F%2Fwww.sciencedirect.com%2Fscience%2Farticle%2Fpii%2FS0045782518305814&rft_id=info%3Aarxiv%2F1902.09953&rft_id=info%3Abibcode%2F2019CMAME.346...85A&rft_id=info%3Adoi%2F10.1016%2Fj.cma.2018.10.048&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Ligações_externas"><span id="Liga.C3.A7.C3.B5es_externas"></span>Ligações externas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Icosaedro&veaction=edit&section=10" title="Editar secção: Ligações externas" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Icosaedro&action=edit&section=10" title="Editar código-fonte da secção: Ligações externas"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20091014103156/http://www.uff.br/cdme/platonicos/platonicos-html/icosaedro-br.html">Modelo 3D Interativo do Icosaedro</a></li> <li><a rel="nofollow" class="external text" href="http://www.mathconsult.ch/showroom/unipoly/">Os poliedros uniformes</a></li> <li><a rel="nofollow" class="external text" href="http://www.georgehart.com/virtual-polyhedra/vp.html">Poliedros em realidade virtual</a> A enciclopédia dos poliedros.</li> <li><a rel="nofollow" class="external text" href="http://www.korthalsaltes.com/">Paper Models of Polyhedra</a> Várias ligações</li> <li><a rel="nofollow" class="external text" href="http://www.rwgrayprojects.com/rbfnotes/maps/graymap1.html">O icosaedro e os mapas de Fuller</a></li></ul> <p><br /> </p> <div role="navigation" class="navbox" aria-labelledby="Poliedro_convexo" style="padding:3px"><table class="nowraplinks collapsible collapsible navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div class="plainlinks hlist navbar mini"><ul><li class="nv-ver"><a href="/wiki/Predefini%C3%A7%C3%A3o:Poliedros_convexos" title="Predefinição:Poliedros convexos"><abbr title="Ver esta predefinição" style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;">v</abbr></a></li><li class="nv-discutir"><a href="/w/index.php?title=Predefini%C3%A7%C3%A3o_Discuss%C3%A3o:Poliedros_convexos&action=edit&redlink=1" class="new" title="Predefinição Discussão:Poliedros convexos (página não existe)"><abbr title="Discutir esta predefinição" style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;">d</abbr></a></li><li class="nv-editar"><a class="external text" href="https://pt.wikipedia.org/w/index.php?title=Predefini%C3%A7%C3%A3o:Poliedros_convexos&action=edit"><abbr title="Editar esta predefinição" style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;">e</abbr></a></li></ul></div><div id="Poliedro_convexo" style="font-size:114%;margin:0 4em"><a href="/wiki/Pol%C3%ADtopo_convexo" title="Polítopo convexo">Poliedro convexo</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/S%C3%B3lido_plat%C3%B3nico" title="Sólido platónico">Sólidos platônicos</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Tetraedro" title="Tetraedro">Tetraedro</a></li> <li><a href="/wiki/Cubo" title="Cubo">Cubo</a></li> <li><a href="/wiki/Octaedro" title="Octaedro">Octaedro</a></li> <li><a href="/wiki/Dodecaedro" title="Dodecaedro">Dodecaedro</a></li> <li><a class="mw-selflink selflink">Icosaedro</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/S%C3%B3lido_de_Arquimedes" title="Sólido de Arquimedes">Sólidos de Arquimedes</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Tetraedro_truncado" title="Tetraedro truncado">Tetraedro truncado</a></li> <li><a href="/wiki/Cuboctaedro" title="Cuboctaedro">Cuboctaedro</a></li> <li><a href="/wiki/Cubo_truncado" title="Cubo truncado">Cubo truncado</a></li> <li><a href="/wiki/Octaedro_truncado" title="Octaedro truncado">Octaedro truncado</a></li> <li><a href="/wiki/Rombicuboctaedro" title="Rombicuboctaedro">Rombicuboctaedro</a></li> <li><a href="/wiki/Cuboctaedro_truncado" title="Cuboctaedro truncado">Cuboctaedro truncado</a></li> <li><a href="/wiki/Cubo_snub" title="Cubo snub">Cubo snub</a></li> <li><a href="/wiki/Icosidodecaedro" title="Icosidodecaedro">Icosidodecaedro</a></li> <li><a href="/wiki/Dodecaedro_truncado" title="Dodecaedro truncado">Dodecaedro truncado</a></li> <li><a href="/wiki/Icosaedro_truncado" title="Icosaedro truncado">Icosaedro truncado</a></li> <li><a href="/wiki/Rombicosidodecaedro" title="Rombicosidodecaedro">Rombicosidodecaedro</a></li> <li><a href="/wiki/Icosidodecaedro_truncado" title="Icosidodecaedro truncado">Icosidodecaedro truncado</a></li> <li><a href="/wiki/Dodecaedro_torcido" title="Dodecaedro torcido">Dodecaedro torcido</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/S%C3%B3lidos_de_Catalan" title="Sólidos de Catalan">Sólidos de Catalan</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Tetraedro_triakis" title="Tetraedro triakis">Tetraedro triakis</a></li> <li><a href="/wiki/Dodecaedro_r%C3%B4mbico" title="Dodecaedro rômbico">Dodecaedro rômbico</a></li> <li><a href="/wiki/Octaedro_triakis" title="Octaedro triakis">Octaedro triakis</a></li> <li><a href="/wiki/Hexaedro_tetrakis" title="Hexaedro tetrakis">Hexaedro tetrakis</a></li> <li><a href="/wiki/Icositetraedro_deltoidal" title="Icositetraedro deltoidal">Icositetraedro deltoidal</a></li> <li><a href="/wiki/Dodecaedro_disdiakis" title="Dodecaedro disdiakis">Dodecaedro disdiakis</a></li> <li><a href="/wiki/Icositetraedro_pentagonal" title="Icositetraedro pentagonal">Icositetraedro pentagonal</a></li> <li><a href="/wiki/Triacontaedro_r%C3%B4mbico" title="Triacontaedro rômbico">Triacontaedro rômbico</a></li> <li><a href="/wiki/Icosaedro_triakis" title="Icosaedro triakis">Icosaedro triakis</a></li> <li><a href="/wiki/Dodecaedro_pentakis" title="Dodecaedro pentakis">Dodecaedro pentakis</a></li> <li><a href="/wiki/Hexecontaedro_deltoidal" title="Hexecontaedro deltoidal">Hexecontaedro deltoidal</a></li> <li><a href="/wiki/Triacontaedro_disdiakis" title="Triacontaedro disdiakis">Triacontaedro disdiakis</a></li> <li><a href="/wiki/Hexecontaedro_pentagonal" title="Hexecontaedro pentagonal">Hexecontaedro pentagonal</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Diédricos regulares</th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><i><a href="/w/index.php?title=Diedro_(poliedro)&action=edit&redlink=1" class="new" title="Diedro (poliedro) (página não existe)">diedro</a></i></li> <li><i><a href="/w/index.php?title=Triedro_(poliedro)&action=edit&redlink=1" class="new" title="Triedro (poliedro) (página não existe)">triedro</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Diédricos uniformes</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 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:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Prisma" title="Prisma">Prisma</a></li> <li><a href="/wiki/Antiprisma" title="Antiprisma">Antiprisma</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Duais:</th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Bipir%C3%A2mide" title="Bipirâmide">Bipirâmide</a></li> <li><a href="/wiki/Trapezoedro" title="Trapezoedro">Trapezoedro</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Outros diédricos</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Pir%C3%A2mide" title="Pirâmide">Pirâmide</a></li> <li><a href="/w/index.php?title=Trapezoedro_truncado&action=edit&redlink=1" class="new" title="Trapezoedro truncado (página não existe)">Trapezoedro truncado</a></li> <li><a href="/w/index.php?title=Bipir%C3%A2mide_giro-alongada&action=edit&redlink=1" class="new" title="Bipirâmide giro-alongada (página não existe)">Bipirâmide giro-alongada</a></li> <li><a href="/wiki/C%C3%BApula_(geometria)" title="Cúpula (geometria)">Cúpula</a></li> <li><a href="/w/index.php?title=Bic%C3%BApula_(geometria)&action=edit&redlink=1" class="new" title="Bicúpula (geometria) (página não existe)">Bicúpula</a></li> <li><a href="/wiki/Tronco_de_bases_paralelas" class="mw-redirect" title="Tronco de bases paralelas">Tronco de bases paralelas</a></li> <li><a href="/w/index.php?title=Rotunda_(geometria)&action=edit&redlink=1" class="new" title="Rotunda (geometria) (página não existe)">Rotunda</a></li> <li><a href="/w/index.php?title=Birotunda&action=edit&redlink=1" class="new" title="Birotunda (página não existe)">Birotunda</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>Poliedros degenerados estão em <i>itálico</i>.</div></td></tr></tbody></table></div> <table class="noprint" style="border-top:none; border-bottom:none; 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