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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">Inizio</div> </a> </li> <li id="toc-Il_cubo_in_geometria_analitica" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Il_cubo_in_geometria_analitica"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Il cubo in geometria analitica</span> </div> </a> <ul id="toc-Il_cubo_in_geometria_analitica-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Parametri_metrici" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Parametri_metrici"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Parametri metrici</span> </div> </a> <button aria-controls="toc-Parametri_metrici-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>Attiva/disattiva la sottosezione Parametri metrici</span> </button> <ul id="toc-Parametri_metrici-sublist" class="vector-toc-list"> <li id="toc-Rapporto_volume/superficie" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Rapporto_volume/superficie"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Rapporto volume/superficie</span> </div> </a> <ul id="toc-Rapporto_volume/superficie-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Poliedro_duale" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Poliedro_duale"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Poliedro duale</span> </div> </a> <ul id="toc-Poliedro_duale-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Simmetrie" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Simmetrie"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Simmetrie</span> </div> </a> <ul id="toc-Simmetrie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relazioni_con_gli_altri_solidi_platonici" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Relazioni_con_gli_altri_solidi_platonici"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Relazioni con gli altri solidi platonici</span> </div> </a> <button aria-controls="toc-Relazioni_con_gli_altri_solidi_platonici-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>Attiva/disattiva la sottosezione Relazioni con gli altri solidi platonici</span> </button> <ul id="toc-Relazioni_con_gli_altri_solidi_platonici-sublist" class="vector-toc-list"> <li id="toc-Tetraedri_in_un_cubo" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Tetraedri_in_un_cubo"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Tetraedri in un cubo</span> </div> </a> <ul id="toc-Tetraedri_in_un_cubo-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cubi_in_un_dodecaedro" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cubi_in_un_dodecaedro"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Cubi in un dodecaedro</span> </div> </a> <ul id="toc-Cubi_in_un_dodecaedro-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Tassellazione_dello_spazio" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tassellazione_dello_spazio"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Tassellazione dello spazio</span> </div> </a> <ul id="toc-Tassellazione_dello_spazio-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Altro" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Altro"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Altro</span> </div> </a> <ul id="toc-Altro-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Voci_correlate" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Voci_correlate"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Voci correlate</span> </div> </a> <ul id="toc-Voci_correlate-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Altri_progetti" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Altri_progetti"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Altri progetti</span> </div> </a> <ul id="toc-Altri_progetti-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Collegamenti_esterni" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Collegamenti_esterni"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Collegamenti esterni</span> </div> </a> <ul id="toc-Collegamenti_esterni-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="Indice" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Indice" > <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="Mostra/Nascondi l'indice" > <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">Mostra/Nascondi l'indice</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">Cubo</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="Vai a una voce in un'altra lingua. Disponibile in 105 lingue" > <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-105" 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">105 lingue</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/Kubus" title="Kubus - afrikaans" lang="af" hreflang="af" data-title="Kubus" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8A%AD%E1%8B%A9%E1%89%A5" title="ክዩብ - amarico" lang="am" hreflang="am" data-title="ክዩብ" data-language-autonym="አማርኛ" data-language-local-name="amarico" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Cubo" title="Cubo - aragonese" lang="an" hreflang="an" data-title="Cubo" data-language-autonym="Aragonés" data-language-local-name="aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D9%83%D8%B9%D8%A8" title="مكعب - arabo" lang="ar" hreflang="ar" data-title="مكعب" data-language-autonym="العربية" data-language-local-name="arabo" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D9%85%D9%83%D8%B9%D8%A8" title="مكعب - arabo marocchino" lang="ary" hreflang="ary" data-title="مكعب" data-language-autonym="الدارجة" data-language-local-name="arabo marocchino" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Hexaedru" title="Hexaedru - asturiano" lang="ast" hreflang="ast" data-title="Hexaedru" data-language-autonym="Asturianu" data-language-local-name="asturiano" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Kub" title="Kub - azerbaigiano" lang="az" hreflang="az" data-title="Kub" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaigiano" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%DA%A9%DB%86%D8%A8" title="کۆب - South Azerbaijani" lang="azb" hreflang="azb" data-title="کۆب" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9A%D1%83%D0%B1" title="Куб - baschiro" lang="ba" hreflang="ba" data-title="Куб" data-language-autonym="Башҡортса" data-language-local-name="baschiro" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9A%D1%83%D0%B1" title="Куб - bielorusso" lang="be" hreflang="be" data-title="Куб" data-language-autonym="Беларуская" data-language-local-name="bielorusso" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9A%D1%83%D0%B1" title="Куб - bulgaro" lang="bg" hreflang="bg" data-title="Куб" data-language-autonym="Български" data-language-local-name="bulgaro" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Kocka" title="Kocka - bosniaco" lang="bs" hreflang="bs" data-title="Kocka" data-language-autonym="Bosanski" data-language-local-name="bosniaco" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Cub" title="Cub - catalano" lang="ca" hreflang="ca" data-title="Cub" data-language-autonym="Català" data-language-local-name="catalano" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%B4%DB%95%D8%B4%D9%BE%D8%A7%DA%B5%D9%88%D9%88" title="شەشپاڵوو - curdo centrale" lang="ckb" hreflang="ckb" data-title="شەشپاڵوو" data-language-autonym="کوردی" data-language-local-name="curdo centrale" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Krychle" title="Krychle - ceco" lang="cs" hreflang="cs" data-title="Krychle" data-language-autonym="Čeština" data-language-local-name="ceco" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9A%D1%83%D0%B1" title="Куб - ciuvascio" lang="cv" hreflang="cv" data-title="Куб" data-language-autonym="Чӑвашла" data-language-local-name="ciuvascio" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Ciwb" title="Ciwb - gallese" lang="cy" hreflang="cy" data-title="Ciwb" data-language-autonym="Cymraeg" data-language-local-name="gallese" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Terning" title="Terning - danese" lang="da" hreflang="da" data-title="Terning" data-language-autonym="Dansk" data-language-local-name="danese" 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/W%C3%BCrfel_(Geometrie)" title="Würfel (Geometrie) - tedesco" lang="de" hreflang="de" data-title="Würfel (Geometrie)" data-language-autonym="Deutsch" data-language-local-name="tedesco" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9A%CF%8D%CE%B2%CE%BF%CF%82" title="Κύβος - greco" lang="el" hreflang="el" data-title="Κύβος" data-language-autonym="Ελληνικά" data-language-local-name="greco" 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/Cube" title="Cube - inglese" lang="en" hreflang="en" data-title="Cube" data-language-autonym="English" data-language-local-name="inglese" 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/Kubo_(geometrio)" title="Kubo (geometrio) - esperanto" lang="eo" hreflang="eo" data-title="Kubo (geometrio)" 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/Cubo" title="Cubo - spagnolo" lang="es" hreflang="es" data-title="Cubo" data-language-autonym="Español" data-language-local-name="spagnolo" 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/Kuup" title="Kuup - estone" lang="et" hreflang="et" data-title="Kuup" data-language-autonym="Eesti" data-language-local-name="estone" 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/Kubo" title="Kubo - basco" lang="eu" hreflang="eu" data-title="Kubo" 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/%D9%85%DA%A9%D8%B9%D8%A8" title="مکعب - persiano" lang="fa" hreflang="fa" data-title="مکعب" data-language-autonym="فارسی" data-language-local-name="persiano" 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/Kuutio" title="Kuutio - finlandese" lang="fi" hreflang="fi" data-title="Kuutio" data-language-autonym="Suomi" data-language-local-name="finlandese" 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/Cube" title="Cube - francese" lang="fr" hreflang="fr" data-title="Cube" data-language-autonym="Français" data-language-local-name="francese" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Tiarling_(Geometrii)" title="Tiarling (Geometrii) - frisone settentrionale" lang="frr" hreflang="frr" data-title="Tiarling (Geometrii)" data-language-autonym="Nordfriisk" data-language-local-name="frisone settentrionale" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Ci%C3%BAb" title="Ciúb - irlandese" lang="ga" hreflang="ga" data-title="Ciúb" data-language-autonym="Gaeilge" data-language-local-name="irlandese" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E7%AB%8B%E6%96%B9%E9%AB%94" title="立方體 - gan" lang="gan" hreflang="gan" data-title="立方體" data-language-autonym="贛語" data-language-local-name="gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Cubo" title="Cubo - galiziano" lang="gl" hreflang="gl" data-title="Cubo" data-language-autonym="Galego" data-language-local-name="galiziano" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%B8%E0%AA%AE%E0%AA%98%E0%AA%A8" title="સમઘન - gujarati" lang="gu" hreflang="gu" data-title="સમઘન" data-language-autonym="ગુજરાતી" data-language-local-name="gujarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%95%D7%91%D7%99%D7%99%D7%94" title="קובייה - ebraico" lang="he" hreflang="he" data-title="קובייה" data-language-autonym="עברית" data-language-local-name="ebraico" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%98%E0%A4%A8_(%E0%A4%9C%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AE%E0%A4%BF%E0%A4%A4%E0%A4%BF)" title="घन (ज्यामिति) - hindi" lang="hi" hreflang="hi" data-title="घन (ज्यामिति)" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Kocka" title="Kocka - croato" lang="hr" hreflang="hr" data-title="Kocka" data-language-autonym="Hrvatski" data-language-local-name="croato" 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/Kocka" title="Kocka - ungherese" lang="hu" hreflang="hu" data-title="Kocka" data-language-autonym="Magyar" data-language-local-name="ungherese" 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%BD%D5%B8%D6%80%D5%A1%D5%B6%D5%A1%D6%80%D5%A4" title="Խորանարդ - armeno" lang="hy" hreflang="hy" data-title="Խորանարդ" data-language-autonym="Հայերեն" data-language-local-name="armeno" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hyw mw-list-item"><a href="https://hyw.wikipedia.org/wiki/%D4%BD%D5%B8%D6%80%D5%A1%D5%B6%D5%A1%D6%80%D5%A4" title="Խորանարդ - Western Armenian" lang="hyw" hreflang="hyw" data-title="Խորանարդ" data-language-autonym="Արեւմտահայերէն" data-language-local-name="Western Armenian" class="interlanguage-link-target"><span>Արեւմտահայերէն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kubus" title="Kubus - indonesiano" lang="id" hreflang="id" data-title="Kubus" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiano" 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/Kubo" title="Kubo - ido" lang="io" hreflang="io" data-title="Kubo" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%AD%A3%E5%85%AD%E9%9D%A2%E4%BD%93" title="正六面体 - giapponese" lang="ja" hreflang="ja" data-title="正六面体" data-language-autonym="日本語" data-language-local-name="giapponese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Kyuub" title="Kyuub - creolo giamaicano" lang="jam" hreflang="jam" data-title="Kyuub" data-language-autonym="Patois" data-language-local-name="creolo giamaicano" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Kubuk" title="Kubuk - giavanese" lang="jv" hreflang="jv" data-title="Kubuk" data-language-autonym="Jawa" data-language-local-name="giavanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%99%E1%83%A3%E1%83%91%E1%83%98" title="კუბი - georgiano" lang="ka" hreflang="ka" data-title="კუბი" data-language-autonym="ქართული" data-language-local-name="georgiano" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D1%83%D0%B1" title="Куб - kazako" lang="kk" hreflang="kk" data-title="Куб" data-language-autonym="Қазақша" data-language-local-name="kazako" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%98%E0%B2%A8_(%E0%B2%86%E0%B2%95%E0%B3%83%E0%B2%A4%E0%B2%BF)" title="ಘನ (ಆಕೃತಿ) - kannada" lang="kn" hreflang="kn" data-title="ಘನ (ಆಕೃತಿ)" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A0%95%EC%9C%A1%EB%A9%B4%EC%B2%B4" title="정육면체 - coreano" lang="ko" hreflang="ko" data-title="정육면체" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9A%D1%83%D0%B1" title="Куб - kirghiso" lang="ky" hreflang="ky" data-title="Куб" data-language-autonym="Кыргызча" data-language-local-name="kirghiso" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Cubus" title="Cubus - latino" lang="la" hreflang="la" data-title="Cubus" data-language-autonym="Latina" data-language-local-name="latino" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Wierfel" title="Wierfel - lussemburghese" lang="lb" hreflang="lb" data-title="Wierfel" data-language-autonym="Lëtzebuergesch" data-language-local-name="lussemburghese" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%A5%E0%BA%B9%E0%BA%81%E0%BA%9A%E0%BA%B2%E0%BA%94" title="ລູກບາດ - lao" lang="lo" hreflang="lo" data-title="ລູກບາດ" data-language-autonym="ລາວ" data-language-local-name="lao" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Kubas" title="Kubas - lituano" lang="lt" hreflang="lt" data-title="Kubas" 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/Kubs" title="Kubs - lettone" lang="lv" hreflang="lv" data-title="Kubs" data-language-autonym="Latviešu" data-language-local-name="lettone" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mdf mw-list-item"><a href="https://mdf.wikipedia.org/wiki/%D0%9A%D1%83%D0%B1%D1%81%D1%8C" title="Кубсь - moksha" lang="mdf" hreflang="mdf" data-title="Кубсь" data-language-autonym="Мокшень" data-language-local-name="moksha" class="interlanguage-link-target"><span>Мокшень</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Goba_(je%C3%B4metria)" title="Goba (jeômetria) - malgascio" lang="mg" hreflang="mg" data-title="Goba (jeômetria)" data-language-autonym="Malagasy" data-language-local-name="malgascio" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mhr mw-list-item"><a href="https://mhr.wikipedia.org/wiki/%D0%9A%D1%83%D0%B1" title="Куб - Eastern Mari" lang="mhr" hreflang="mhr" data-title="Куб" data-language-autonym="Олык марий" data-language-local-name="Eastern Mari" class="interlanguage-link-target"><span>Олык марий</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D0%BE%D1%86%D0%BA%D0%B0" title="Коцка - macedone" lang="mk" hreflang="mk" data-title="Коцка" data-language-autonym="Македонски" data-language-local-name="macedone" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B8%E0%B4%AE%E0%B4%9A%E0%B4%A4%E0%B5%81%E0%B4%B0%E0%B4%95%E0%B5%8D%E0%B4%95%E0%B4%9F%E0%B5%8D%E0%B4%9F" title="സമചതുരക്കട്ട - malayalam" lang="ml" hreflang="ml" data-title="സമചതുരക്കട്ട" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%98%E0%A4%A8_(%E0%A4%AD%E0%A5%82%E0%A4%AE%E0%A4%BF%E0%A4%A4%E0%A5%80)" title="घन (भूमिती) - marathi" lang="mr" hreflang="mr" data-title="घन (भूमिती)" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Kubus" title="Kubus - malese" lang="ms" hreflang="ms" data-title="Kubus" data-language-autonym="Bahasa Melayu" data-language-local-name="malese" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/W%C3%B6rpel_(Geometrie)" title="Wörpel (Geometrie) - basso tedesco" lang="nds" hreflang="nds" data-title="Wörpel (Geometrie)" data-language-autonym="Plattdüütsch" data-language-local-name="basso tedesco" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Kubus_(ruimtelijke_figuur)" title="Kubus (ruimtelijke figuur) - olandese" lang="nl" hreflang="nl" data-title="Kubus (ruimtelijke figuur)" data-language-autonym="Nederlands" data-language-local-name="olandese" 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/Kube" title="Kube - norvegese nynorsk" lang="nn" hreflang="nn" data-title="Kube" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegese 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/Kube" title="Kube - norvegese bokmål" lang="nb" hreflang="nb" data-title="Kube" data-language-autonym="Norsk bokmål" data-language-local-name="norvegese 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/Cube" title="Cube - occitano" lang="oc" hreflang="oc" data-title="Cube" data-language-autonym="Occitan" data-language-local-name="occitano" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Garjii" title="Garjii - oromo" lang="om" hreflang="om" data-title="Garjii" data-language-autonym="Oromoo" data-language-local-name="oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%98%E0%A8%A3_(%E0%A8%96%E0%A9%87%E0%A8%A4%E0%A8%B0%E0%A8%AE%E0%A8%BF%E0%A8%A4%E0%A9%80)" title="ਘਣ (ਖੇਤਰਮਿਤੀ) - punjabi" lang="pa" hreflang="pa" data-title="ਘਣ (ਖੇਤਰਮਿਤੀ)" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Sze%C5%9Bcian_(geometria)" title="Sześcian (geometria) - polacco" lang="pl" hreflang="pl" data-title="Sześcian (geometria)" data-language-autonym="Polski" data-language-local-name="polacco" 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/Cubo" title="Cubo - piemontese" lang="pms" hreflang="pms" data-title="Cubo" data-language-autonym="Piemontèis" data-language-local-name="piemontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%85%DA%A9%D8%B9%D8%A8" title="مکعب - Western Punjabi" lang="pnb" hreflang="pnb" data-title="مکعب" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%AF%D8%B1%DB%90%D9%8A%DA%81_(%D9%85%DB%90%DA%86%D9%BE%D9%88%D9%87%D9%86%D9%87)" title="درېيځ (مېچپوهنه) - pashto" lang="ps" hreflang="ps" data-title="درېيځ (مېچپوهنه)" data-language-autonym="پښتو" data-language-local-name="pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Cubo" title="Cubo - portoghese" lang="pt" hreflang="pt" data-title="Cubo" data-language-autonym="Português" data-language-local-name="portoghese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Mach%27ina" title="Mach'ina - quechua" lang="qu" hreflang="qu" data-title="Mach'ina" data-language-autonym="Runa Simi" data-language-local-name="quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Cub" title="Cub - rumeno" lang="ro" hreflang="ro" data-title="Cub" data-language-autonym="Română" data-language-local-name="rumeno" 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%9A%D1%83%D0%B1" title="Куб - russo" lang="ru" hreflang="ru" data-title="Куб" data-language-autonym="Русский" data-language-local-name="russo" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%9A%D1%83%D0%B1" title="Куб - sacha" lang="sah" hreflang="sah" data-title="Куб" data-language-autonym="Саха тыла" data-language-local-name="sacha" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Cubbu" title="Cubbu - siciliano" lang="scn" hreflang="scn" data-title="Cubbu" data-language-autonym="Sicilianu" data-language-local-name="siciliano" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Cube" title="Cube - scozzese" lang="sco" hreflang="sco" data-title="Cube" data-language-autonym="Scots" data-language-local-name="scozzese" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-se mw-list-item"><a href="https://se.wikipedia.org/wiki/Gu%C4%91ahas" title="Guđahas - sami del nord" lang="se" hreflang="se" data-title="Guđahas" data-language-autonym="Davvisámegiella" data-language-local-name="sami del nord" class="interlanguage-link-target"><span>Davvisámegiella</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Kocka" title="Kocka - serbo-croato" lang="sh" hreflang="sh" data-title="Kocka" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-croato" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%9D%E0%B6%B1%E0%B6%9A%E0%B6%BA" title="ඝනකය - singalese" lang="si" hreflang="si" data-title="ඝනකය" data-language-autonym="සිංහල" data-language-local-name="singalese" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Cube" title="Cube - Simple English" lang="en-simple" hreflang="en-simple" data-title="Cube" 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/Kocka" title="Kocka - slovacco" lang="sk" hreflang="sk" data-title="Kocka" data-language-autonym="Slovenčina" data-language-local-name="slovacco" 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/Kocka" title="Kocka - sloveno" lang="sl" hreflang="sl" data-title="Kocka" data-language-autonym="Slovenščina" data-language-local-name="sloveno" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Sedjibeke_(shaxan)" title="Sedjibeke (shaxan) - somalo" lang="so" hreflang="so" data-title="Sedjibeke (shaxan)" data-language-autonym="Soomaaliga" data-language-local-name="somalo" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Kubi_(gjeometri)" title="Kubi (gjeometri) - albanese" lang="sq" hreflang="sq" data-title="Kubi (gjeometri)" data-language-autonym="Shqip" data-language-local-name="albanese" 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%9A%D0%BE%D1%86%D0%BA%D0%B0" title="Коцка - serbo" lang="sr" hreflang="sr" data-title="Коцка" data-language-autonym="Српски / srpski" data-language-local-name="serbo" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Kubes" title="Kubes - sundanese" lang="su" hreflang="su" data-title="Kubes" data-language-autonym="Sunda" data-language-local-name="sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Kub" title="Kub - svedese" lang="sv" hreflang="sv" data-title="Kub" data-language-autonym="Svenska" data-language-local-name="svedese" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Mchemraba" title="Mchemraba - swahili" lang="sw" hreflang="sw" data-title="Mchemraba" data-language-autonym="Kiswahili" data-language-local-name="swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AE%A9%E0%AE%9A%E0%AE%A4%E0%AF%81%E0%AE%B0%E0%AE%AE%E0%AF%8D" title="கனசதுரம் - tamil" lang="ta" hreflang="ta" data-title="கனசதுரம்" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%95%E0%B1%8D%E0%B0%AF%E0%B1%82%E0%B0%AC%E0%B1%8D" title="క్యూబ్ - telugu" lang="te" hreflang="te" data-title="క్యూబ్" data-language-autonym="తెలుగు" data-language-local-name="telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%97%E0%B8%A3%E0%B8%87%E0%B8%A5%E0%B8%B9%E0%B8%81%E0%B8%9A%E0%B8%B2%E0%B8%A8%E0%B8%81%E0%B9%8C" title="ทรงลูกบาศก์ - thailandese" lang="th" hreflang="th" data-title="ทรงลูกบาศก์" data-language-autonym="ไทย" data-language-local-name="thailandese" 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/K%C3%BCp" title="Küp - turco" lang="tr" hreflang="tr" data-title="Küp" data-language-autonym="Türkçe" data-language-local-name="turco" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D1%83%D0%B1" title="Куб - ucraino" lang="uk" hreflang="uk" data-title="Куб" data-language-autonym="Українська" data-language-local-name="ucraino" 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/%D9%85%DA%A9%D8%B9%D8%A8" title="مکعب - urdu" lang="ur" hreflang="ur" data-title="مکعب" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Kub" title="Kub - uzbeco" lang="uz" hreflang="uz" data-title="Kub" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbeco" 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/Kh%E1%BB%91i_l%E1%BA%ADp_ph%C6%B0%C6%A1ng" title="Khối lập phương - vietnamita" lang="vi" hreflang="vi" data-title="Khối lập phương" 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-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Kubo" title="Kubo - waray" lang="war" hreflang="war" data-title="Kubo" data-language-autonym="Winaray" data-language-local-name="waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%AB%8B%E6%96%B9%E4%BD%93" title="立方体 - wu" lang="wuu" hreflang="wuu" data-title="立方体" data-language-autonym="吴语" data-language-local-name="wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%AB%8B%E6%96%B9%E9%AB%94" title="立方體 - cinese" lang="zh" hreflang="zh" data-title="立方體" data-language-autonym="中文" data-language-local-name="cinese" 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_lio%CC%8Dk-bi%C4%81n-th%C3%A9" title="Chiàⁿ lio̍k-biān-thé - min nan" lang="nan" hreflang="nan" data-title="Chiàⁿ lio̍k-biān-thé" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="min nan" 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%AD%A3%E6%96%B9%E9%AB%94" title="正方體 - cantonese" lang="yue" hreflang="yue" data-title="正方體" data-language-autonym="粵語" data-language-local-name="cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/IGcikiva" title="IGcikiva - zulu" lang="zu" hreflang="zu" data-title="IGcikiva" data-language-autonym="IsiZulu" data-language-local-name="zulu" class="interlanguage-link-target"><span>IsiZulu</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/Q812880#sitelinks-wikipedia" title="Modifica collegamenti interlinguistici" class="wbc-editpage">Modifica collegamenti</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="Namespace"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Cubo" title="Vedi la voce [c]" accesskey="c"><span>Voce</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Discussione:Cubo" rel="discussion" title="Vedi le discussioni relative a questa pagina [t]" accesskey="t"><span>Discussione</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Cambia versione linguistica" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">italiano</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Visite"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Cubo"><span>Leggi</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Cubo&veaction=edit" title="Modifica questa pagina [v]" accesskey="v"><span>Modifica</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Cubo&action=edit" title="Modifica il wikitesto di questa pagina [e]" accesskey="e"><span>Modifica wikitesto</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Cubo&action=history" title="Versioni precedenti di questa pagina [h]" accesskey="h"><span>Cronologia</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Strumenti pagine"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Strumenti" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Strumenti</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Strumenti</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">sposta nella barra laterale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">nascondi</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Altre opzioni" > <div class="vector-menu-heading"> Azioni </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Cubo"><span>Leggi</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Cubo&veaction=edit" title="Modifica questa pagina [v]" accesskey="v"><span>Modifica</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Cubo&action=edit" title="Modifica il wikitesto di questa pagina [e]" accesskey="e"><span>Modifica wikitesto</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Cubo&action=history"><span>Cronologia</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Generale </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Speciale:PuntanoQui/Cubo" title="Elenco di tutte le pagine che sono collegate a questa [j]" accesskey="j"><span>Puntano qui</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Speciale:ModificheCorrelate/Cubo" rel="nofollow" title="Elenco delle ultime modifiche alle pagine collegate a questa [k]" accesskey="k"><span>Modifiche correlate</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Cubo&oldid=144299127" title="Collegamento permanente a questa versione di questa pagina"><span>Link permanente</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Cubo&action=info" title="Ulteriori informazioni su questa pagina"><span>Informazioni pagina</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Speciale:Cita&page=Cubo&id=144299127&wpFormIdentifier=titleform" title="Informazioni su come citare questa pagina"><span>Cita questa voce</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Speciale:UrlShortener&url=https%3A%2F%2Fit.wikipedia.org%2Fwiki%2FCubo"><span>Ottieni URL breve</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Speciale:QrCode&url=https%3A%2F%2Fit.wikipedia.org%2Fwiki%2FCubo"><span>Scarica codice QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Stampa/esporta </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Speciale:Libro&bookcmd=book_creator&referer=Cubo"><span>Crea un libro</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Speciale:DownloadAsPdf&page=Cubo&action=show-download-screen"><span>Scarica come PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Cubo&printable=yes" title="Versione stampabile di questa pagina [p]" accesskey="p"><span>Versione stampabile</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In altri progetti </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Cube" hreflang="en"><span>Wikimedia Commons</span></a></li><li class="wb-otherproject-link wb-otherproject-wikiquote mw-list-item"><a href="https://it.wikiquote.org/wiki/Cubo" hreflang="it"><span>Wikiquote</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q812880" title="Collegamento all'elemento connesso dell'archivio dati [g]" accesskey="g"><span>Elemento Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Strumenti pagine"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Aspetto"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header 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">Aspetto</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">sposta nella barra laterale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">nascondi</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">Da Wikipedia, l'enciclopedia libera.</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="it" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r130658281">body:not(.skin-minerva) .mw-parser-output .hatnote.nota-disambigua{clear:both;margin-top:0;padding:.05em .5em}</style> <style data-mw-deduplicate="TemplateStyles:r139142988">.mw-parser-output .hatnote-content{align-items:center;display:flex}.mw-parser-output .hatnote-icon{flex-shrink:0}.mw-parser-output .hatnote-icon img{display:flex}.mw-parser-output .hatnote-text{font-style:italic}body:not(.skin-minerva) .mw-parser-output .hatnote{border:1px solid #CCC;display:flex;margin:.5em 0;padding:.2em .5em}body:not(.skin-minerva) .mw-parser-output .hatnote-text{padding-left:.5em}body.skin-minerva .mw-parser-output .hatnote-icon{padding-right:8px}body.skin-minerva .mw-parser-output .hatnote-icon img{height:auto;width:16px}body.skin--responsive .mw-parser-output .hatnote a.new{color:#d73333}body.skin--responsive .mw-parser-output .hatnote a.new:visited{color:#a55858}</style> <div class="hatnote noprint nota-disambigua"> <div class="hatnote-content"><span class="noviewer hatnote-icon" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Nota_disambigua.svg/18px-Nota_disambigua.svg.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Nota_disambigua.svg/27px-Nota_disambigua.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Nota_disambigua.svg/36px-Nota_disambigua.svg.png 2x" data-file-width="200" data-file-height="200" /></span></span> <span class="hatnote-text"><a href="/wiki/Aiuto:Disambiguazione" title="Aiuto:Disambiguazione">Disambiguazione</a> – Se stai cercando altri significati, vedi <b><a href="/wiki/Cubo_(disambigua)" class="mw-disambig" title="Cubo (disambigua)">Cubo (disambigua)</a></b>.</span></div> </div> <style data-mw-deduplicate="TemplateStyles:r143074810">.mw-parser-output .sinottico{background-color:#f8f9fa;border:1px solid #c8ccd1;border-spacing:0;clear:right;float:right;font-size:95%;line-height:1.4em;margin:0 0 1em 1.5em;width:280px}.mw-parser-output .sinottico caption{font-weight:bold}.mw-parser-output .sinottico>tbody>tr>th:not(:only-child),.mw-parser-output .sinottico_annidata>tbody>tr>th:not(:only-child){background-color:#f3f3f3;border-right:1px solid #e5e5e8;text-align:left;vertical-align:top}.mw-parser-output .sinottico>tbody>tr:not(:last-child)>td,.mw-parser-output .sinottico>tbody>tr:not(:last-child)>th,.mw-parser-output .sinottico_annidata>tbody>tr>td,.mw-parser-output .sinottico_annidata>tbody>tr>th{border-bottom:1px solid #e0e0e0}.mw-parser-output .sinottico>tbody>tr>td,.mw-parser-output .sinottico>tbody>tr>th:not(:only-child),.mw-parser-output .sinottico_annidata>tbody>tr>td,.mw-parser-output .sinottico_annidata>tbody>tr>th:not(:only-child){padding:.25em .4em}.mw-parser-output .sinottico>tbody>tr>td,.mw-parser-output .sinottico_annidata>tbody>tr>td{vertical-align:middle}.mw-parser-output .sinottico>tbody>tr>td>hr:only-child{margin:0.4em 0.2em}.mw-parser-output .sinottico ul{margin:0 0 0 1em;padding:0}.mw-parser-output .sinottico_annidata{border-spacing:0;margin:0 -.4em;width:calc(100% + calc(.4em*2))}.mw-parser-output .sinottico_annidata:last-child{margin-bottom:-.2em}.mw-parser-output .sinottico_annidata:last-child>tbody>tr:last-child>td,.mw-parser-output .sinottico_annidata:last-child>tbody>tr:last-child>th{border-bottom:none}.mw-parser-output .sinottico_divisione+.sinottico_divisione>th,.mw-parser-output .sinottico_testata+.sinottico_divisione>th{border-top:2px solid #f8f9fa}.mw-parser-output .sinottico_divisione th{background-color:#eeeeee;padding:.15em .4em;text-align:center}.mw-parser-output .sinottico_piede{text-align:center;font-size:90%;background:#EFEFEF}.mw-parser-output .sinottico_piede2{background-color:white;font-size:xx-small;padding-bottom:0;text-align:right}.mw-parser-output .sinottico_sottotitolo{font-size:80%}.mw-parser-output .sinottico_testata th{background-color:#dedede;font-size:116%;padding:.2em .4em;text-align:center}.mw-parser-output .sinottico_testo_centrale{text-align:center}</style><table class="infobox sinottico" summary="Tabella sinottica che riassume i principali dati del soggetto"><tbody><tr class="sinottico_testata"><th colspan="2" style="background-color: #e7dcc3; color: black;">Cubo</th></tr><tr><td class="sinottico_testo_centrale" colspan="2"><figure class="mw-halign-center" typeof="mw:File/Frameless"><a href="/wiki/File:Hexahedron.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Hexahedron.gif" decoding="async" width="256" height="256" class="mw-file-element" data-file-width="256" data-file-height="256" /></a><figcaption></figcaption></figure></td></tr><tr><th>Tipo</th><td><a href="/wiki/Solido_platonico" title="Solido platonico">Solido platonico</a> </td></tr><tr><th>Forma facce</th><td><a href="/wiki/Quadrato_(geometria)" class="mw-redirect" title="Quadrato (geometria)">Quadrati</a> </td></tr><tr><th>Nº facce</th><td>6 </td></tr><tr><th>Nº spigoli</th><td>12 </td></tr><tr><th>Nº vertici</th><td>8 </td></tr><tr><th><a href="/wiki/Cuspide_(poliedro)" title="Cuspide (poliedro)">Valenze</a> vertici</th><td>3 </td></tr><tr><th><a href="/wiki/Caratteristica_di_Eulero" title="Caratteristica di Eulero">Caratteristica di Eulero</a></th><td>2 </td></tr><tr><th><a href="/wiki/Notazione_di_Wythoff" title="Notazione di Wythoff">Notazione di Wythoff</a></th><td>3 | 2 4 </td></tr><tr><th><a href="/wiki/Notazione_di_Schl%C3%A4fli" title="Notazione di Schläfli">Notazione di Schläfli</a></th><td>{4,3}<br />t{2,4} o {4}×{}<br />tr{2,2}<br />{}×{}×{} = {}<sup>3</sup> </td></tr><tr><th><a href="/wiki/Diagramma_di_Coxeter-Dynkin" title="Diagramma di Coxeter-Dynkin">Diagramma di Coxeter-Dynkin</a></th><td><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span></span> </td></tr><tr><th><a href="/wiki/Simmetria_(matematica)" title="Simmetria (matematica)">Gruppo di simmetria</a></th><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 S_{4}\times \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mo>×</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{4}\times \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce95ce9d295f33dedb1e8d9557f83005568086ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.924ex; height:2.509ex;" alt="{\displaystyle S_{4}\times \mathbb {Z} _{2}}" /></span> </td></tr><tr><th><a href="/wiki/Poliedro_duale" title="Poliedro duale">Duale</a></th><td><a href="/wiki/Ottaedro" title="Ottaedro">Ottaedro</a> </td></tr><tr><th><a href="/wiki/Angolo_diedro" title="Angolo diedro">Angoli diedrali</a></th><td>90° (<a href="/wiki/Angolo_retto" title="Angolo retto">angolo retto</a>) </td></tr><tr><th>Proprietà</th><td><a href="/wiki/Chiralit%C3%A0_(matematica)" title="Chiralità (matematica)">non chirale</a> </td></tr><tr class="sinottico_divisione"><th colspan="2">Politopi correlati</th></tr><tr><td class="sinottico_testo_centrale" colspan="2"><table><tbody><tr><td align="center" style="border: #999999 1px solid;"><figure class="mw-halign-center" typeof="mw:File/Frameless"><a href="/wiki/File:Cube_vertfig_svg.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Cube_vertfig_svg.svg/130px-Cube_vertfig_svg.svg.png" decoding="async" width="130" height="129" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Cube_vertfig_svg.svg/195px-Cube_vertfig_svg.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Cube_vertfig_svg.svg/260px-Cube_vertfig_svg.svg.png 2x" data-file-width="642" data-file-height="639" /></a><figcaption></figcaption></figure><a href="/wiki/Figura_al_vertice" title="Figura al vertice">Figura al vertice</a></td><td align="center" style="border: #999999 1px solid;"><figure class="mw-halign-center" typeof="mw:File/Frameless"><a href="/wiki/File:Octahedron_(vector).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Octahedron_%28vector%29.svg/250px-Octahedron_%28vector%29.svg.png" decoding="async" width="130" height="135" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Octahedron_%28vector%29.svg/330px-Octahedron_%28vector%29.svg.png 2x" data-file-width="480" data-file-height="500" /></a><figcaption></figcaption></figure><a href="/wiki/Poliedro_duale" title="Poliedro duale">Poliedro duale</a></td></tr></tbody></table> </td></tr><tr class="sinottico_divisione"><th colspan="2"><a href="/wiki/Sviluppo_piano_di_un_poliedro" title="Sviluppo piano di un poliedro">Sviluppo piano</a></th></tr><tr><td class="sinottico_testo_centrale" colspan="2"><figure class="mw-halign-center" typeof="mw:File/Frameless"><a href="/wiki/File:Hexahedron_flat_color.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Hexahedron_flat_color.svg/229px-Hexahedron_flat_color.svg.png" decoding="async" width="229" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Hexahedron_flat_color.svg/343px-Hexahedron_flat_color.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Hexahedron_flat_color.svg/458px-Hexahedron_flat_color.svg.png 2x" data-file-width="171" data-file-height="224" /></a><figcaption></figcaption></figure> </td></tr><tr><td class="sinottico_piede2 noprint nomobile metadata" colspan="2"> <a href="/wiki/Template:Poliedro/man" title="Template:Poliedro/man"><span title="Manuale del template Poliedro">Manuale</span></a></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cubo_(Matemateca_-_IME_USP).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Cubo_%28Matemateca_-_IME_USP%29.jpg/290px-Cubo_%28Matemateca_-_IME_USP%29.jpg" decoding="async" width="290" height="129" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Cubo_%28Matemateca_-_IME_USP%29.jpg/435px-Cubo_%28Matemateca_-_IME_USP%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Cubo_%28Matemateca_-_IME_USP%29.jpg/580px-Cubo_%28Matemateca_-_IME_USP%29.jpg 2x" data-file-width="15000" data-file-height="6667" /></a><figcaption>Cubo (<a href="/w/index.php?title=Matemateca_Ime-Usp&action=edit&redlink=1" class="new" title="Matemateca Ime-Usp (la pagina non esiste)">Matemateca Ime-Usp</a>)</figcaption></figure> <p>Il <b>cubo</b> o <b>esaedro regolare</b> è uno dei 5 <a href="/wiki/Solidi_platonici" class="mw-redirect" title="Solidi platonici">solidi platonici</a>, che presenta 6 facce quadrate, 8 vertici e 12 spigoli; in ogni vertice si incontrano tre spigoli i quali sono ortogonali due a due; in ogni vertice si intersecano anche tre facce le quali sono a due a due ortogonali; questo si accorda con il fatto che il <a href="/wiki/Poliedro_duale" title="Poliedro duale">poliedro duale</a> del cubo è l'<a href="/wiki/Ottaedro" title="Ottaedro">ottaedro</a>, che presenta 8 facce triangolari, 6 vertici e 12 spigoli. </p><p>Il cubo è un <a href="/wiki/Parallelepipedo" title="Parallelepipedo">parallelepipedo</a> retto regolare, ed è un caso particolare di <a href="/wiki/Prisma" title="Prisma">prisma</a> quadrato e di <a href="/wiki/Trapezoedro" title="Trapezoedro">trapezoedro</a>. </p><p>Ogni cubo è caratterizzato dalla lunghezza <i>a</i> dei suoi spigoli. Tutti i cubi con gli spigoli della stessa lunghezza sono <a href="/wiki/Congruenza_(geometria)" title="Congruenza (geometria)">congruenti</a>. Un cubo con gli spigoli di lunghezza <i>a</i> sottoposto ad una omotetia di fattore <i>b</i>/<i>a</i> diventa congruente con ogni cubo con gli spigoli di lunghezza <i>b</i>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Il_cubo_in_geometria_analitica">Il cubo in geometria analitica</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cubo&veaction=edit&section=1" title="Modifica la sezione Il cubo in geometria analitica" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cubo&action=edit&section=1" title="Edit section's source code: Il cubo in geometria analitica"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Molte proprietà del cubo sono ottenibili facilmente con strumenti della <a href="/wiki/Geometria_analitica" title="Geometria analitica">geometria analitica</a>. Consideriamo cubi riferiti a una terna di riferimento cartesiana ortogonale, rispetto alla quale il punto variabile dello spazio sia individuato dalla terna <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 (x_{1},x_{2},x_{3})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x_{1},x_{2},x_{3})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c299961b19740135135d0ef0289b16b6095048d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.029ex; height:2.843ex;" alt="{\displaystyle (x_{1},x_{2},x_{3})}" /></span>. </p><p>Un primo cubo che può essere utile considerare è il cubo centrato nell'origine avente i vertici nei punti dati dalle terne riconducibili alla forma (±1,±1,±1); l'insieme dei suoi punti interni è esprimibile come </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 \{(x_{1},x_{2},x_{3})\;|\;-1<x_{i}<1\ \forall i=1,2,3\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mspace width="thickmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mspace width="thickmathspace"></mspace> <mo>−</mo> <mn>1</mn> <mo><</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo><</mo> <mn>1</mn> <mtext> </mtext> <mi mathvariant="normal">∀</mi> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{(x_{1},x_{2},x_{3})\;|\;-1<x_{i}<1\ \forall i=1,2,3\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b53dcac6f222d9dd507ac754ff9eace60a5cd2d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:40.112ex; height:2.843ex;" alt="{\displaystyle \{(x_{1},x_{2},x_{3})\;|\;-1<x_{i}<1\ \forall i=1,2,3\}}" /></span></dd></dl> <p>Un altro cubo che può risultare maneggevole è quello i cui vertici sono dati da terne binarie </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 (b_{1},b_{2},b_{3})\quad {\mbox{con}}\quad b_{i}=0,1\quad {\mbox{per}}\quad i=1,2,3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mspace width="1em"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>con</mtext> </mstyle> </mrow> <mspace width="1em"></mspace> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mspace width="1em"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>per</mtext> </mstyle> </mrow> <mspace width="1em"></mspace> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (b_{1},b_{2},b_{3})\quad {\mbox{con}}\quad b_{i}=0,1\quad {\mbox{per}}\quad i=1,2,3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0382b5c864834a4014cf000a2fa9eaa1511ad232" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:43.758ex; height:2.843ex;" alt="{\displaystyle (b_{1},b_{2},b_{3})\quad {\mbox{con}}\quad b_{i}=0,1\quad {\mbox{per}}\quad i=1,2,3}" /></span></dd></dl> <p>Questo ha come centro <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 (1/2,1/2,1/2)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo>,</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo>,</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (1/2,1/2,1/2)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee64ffe4baa17b79b9011ecef707d9cefc515fa9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.339ex; height:2.843ex;" alt="{\displaystyle (1/2,1/2,1/2)}" /></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Parametri_metrici">Parametri metrici</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cubo&veaction=edit&section=2" title="Modifica la sezione Parametri metrici" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cubo&action=edit&section=2" title="Edit section's source code: Parametri metrici"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>I parametri metrici del cubo con spigoli di lunghezza <i>a</i> sono i seguenti </p> <table class="wikitable"> <tbody><tr> <td>Lunghezza delle diagonali delle facce </td> <td align="center"><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 {2}}\cdot a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mo>⋅</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,{\sqrt {2}}\cdot a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/edd3e35efe892684c097b6344f06c4113f5e88e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.394ex; height:3.009ex;" alt="{\displaystyle \,{\sqrt {2}}\cdot a}" /></span> </td></tr> <tr> <td>Lunghezza delle diagonali del cubo (segmenti che congiungono vertici opposti) </td> <td align="center"><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}}\cdot a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> <mo>⋅</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,{\sqrt {3}}\cdot a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad41570a56e6386c3561e3c4f28c91c36ce67a15" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.394ex; height:2.843ex;" alt="{\displaystyle \,{\sqrt {3}}\cdot a}" /></span> </td></tr> <tr> <td>Distanza minima tra il centro e una faccia </td> <td align="center"><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/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace"></mspace> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,a/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b4ed4c2f8cc733b266de094ec58b4b6fad75e7d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.942ex; height:2.843ex;" alt="{\displaystyle \,a/2}" /></span> </td></tr> <tr> <td>Area della superficie totale </td> <td align="center"><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"> <mspace width="thinmathspace"></mspace> <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/bd39cae86cfd5c9ebe6249bfb76482b92339f52c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.834ex; height:2.676ex;" alt="{\displaystyle \,6a^{2}}" /></span> </td></tr> <tr> <td>Volume </td> <td align="center"><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"> <mspace width="thinmathspace"></mspace> <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/b808b98241052bbff19b6abb8793307dd4cfda2d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.671ex; height:2.676ex;" alt="{\displaystyle \,a^{3}}" /></span> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Rapporto_volume/superficie"><span id="Rapporto_volume.2Fsuperficie"></span>Rapporto volume/superficie</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cubo&veaction=edit&section=3" title="Modifica la sezione Rapporto volume/superficie" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cubo&action=edit&section=3" title="Edit section's source code: Rapporto volume/superficie"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Hexahedron_flat.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Hexahedron_flat.png/120px-Hexahedron_flat.png" decoding="async" width="110" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/a/a4/Hexahedron_flat.png 1.5x" data-file-width="121" data-file-height="162" /></a><figcaption>Sviluppo del cubo</figcaption></figure> <p>Si nota che la costruzione di un cubo materiale utilizzando carta, cartone, fogli di metallo o altro per le 6 facce, ammesso che non si abbia alcuno spreco di materiale, porta al parallelepipedo con il maggiore rapporto fra volume e superficie totale. </p><p>La dimostrazione di questa proprietà di ottimalità richiede il <a href="/wiki/Calcolo_infinitesimale" title="Calcolo infinitesimale">calcolo infinitesimale</a>. </p><p>Un analogo oggetto materiale costruito con facce <a href="/wiki/Rettangolo" title="Rettangolo">rettangolari</a> non tutte <a href="/wiki/Quadrato_(geometria)" class="mw-redirect" title="Quadrato (geometria)">quadrate</a> presenta un rapporto tra volume e superficie totale inferiore. </p> <div class="mw-heading mw-heading2"><h2 id="Poliedro_duale">Poliedro duale</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cubo&veaction=edit&section=4" title="Modifica la sezione Poliedro duale" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cubo&action=edit&section=4" title="Edit section's source code: Poliedro duale"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Il <a href="/wiki/Poliedro_duale" title="Poliedro duale">poliedro duale</a> del cubo è l'<a href="/wiki/Ottaedro_regolare" class="mw-redirect" title="Ottaedro regolare">ottaedro regolare</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Simmetrie">Simmetrie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cubo&veaction=edit&section=5" title="Modifica la sezione Simmetrie" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cubo&action=edit&section=5" title="Edit section's source code: Simmetrie"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Pyriteespagne.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Pyriteespagne.jpg/220px-Pyriteespagne.jpg" decoding="async" width="220" height="208" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Pyriteespagne.jpg/330px-Pyriteespagne.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/04/Pyriteespagne.jpg/440px-Pyriteespagne.jpg 2x" data-file-width="2641" data-file-height="2497" /></a><figcaption>Cristallo cubico di <a href="/wiki/Pirite" title="Pirite">pirite</a></figcaption></figure> <p>Il cubo ha lo stesso tipo di <a href="/wiki/Simmetria_(matematica)" title="Simmetria (matematica)">simmetrie</a> dell'ottaedro, suo duale. Ha 24 simmetrie <a href="/wiki/Rotazione_(matematica)" title="Rotazione (matematica)">rotazionali</a>, cioè che preservano l'<a href="/wiki/Orientazione" title="Orientazione">orientazione</a> dello spazio, più altre 24 simmetrie che non la preservano. Il <a href="/wiki/Gruppo_di_simmetria" class="mw-redirect" title="Gruppo di simmetria">gruppo di simmetria</a> del cubo consta quindi di un totale di 48 elementi. </p><p>Il <a href="/wiki/Sottogruppo" title="Sottogruppo">sottogruppo</a> dato dalle 24 rotazioni è <a href="/wiki/Isomorfismo" title="Isomorfismo">isomorfo</a> al gruppo <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 S_{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc1632bc1d95d33ccb5473b9d8cc333c2dd0d13a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.479ex; height:2.509ex;" alt="{\displaystyle S_{4}}" /></span> delle <a href="/wiki/Permutazione" title="Permutazione">permutazioni</a> di 4 elementi. Vi è infatti esattamente una rotazione che realizza ogni possibile permutazione delle 4 coppie di vertici opposti. </p><p>Il gruppo totale di simmetria è isomorfo al prodotto <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 S_{4}\times \mathbb {Z} /_{2\mathbb {Z} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{4}\times \mathbb {Z} /_{2\mathbb {Z} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07fdd6f7c5dedc5d4bb6bd74a4619a6d0f59e4dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.183ex; height:3.009ex;" alt="{\displaystyle S_{4}\times \mathbb {Z} /_{2\mathbb {Z} }}" /></span> di <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 S_{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc1632bc1d95d33ccb5473b9d8cc333c2dd0d13a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.479ex; height:2.509ex;" alt="{\displaystyle S_{4}}" /></span> con un <a href="/wiki/Gruppo_ciclico" title="Gruppo ciclico">gruppo ciclico</a> con 2 elementi. </p> <div class="mw-heading mw-heading2"><h2 id="Relazioni_con_gli_altri_solidi_platonici">Relazioni con gli altri solidi platonici</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cubo&veaction=edit&section=6" title="Modifica la sezione Relazioni con gli altri solidi platonici" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cubo&action=edit&section=6" title="Edit section's source code: Relazioni con gli altri solidi platonici"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Tetraedri_in_un_cubo">Tetraedri in un cubo</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cubo&veaction=edit&section=7" title="Modifica la sezione Tetraedri in un cubo" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cubo&action=edit&section=7" title="Edit section's source code: Tetraedri in un cubo"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Cube_vertfig.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Cube_vertfig.png/220px-Cube_vertfig.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Cube_vertfig.png/330px-Cube_vertfig.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Cube_vertfig.png/440px-Cube_vertfig.png 2x" data-file-width="600" data-file-height="600" /></a><figcaption>Tre spigoli di un tetraedro inscritto nel cubo, lati di una faccia triangolare.</figcaption></figure> <p>In un cubo possono essere inscritti cinque <a href="/wiki/Tetraedri" class="mw-redirect" title="Tetraedri">tetraedri</a>; al centro, tra i quattro tetraedri ai vertici, insiste esattamente un tetraedro perfettamente inscritto; i vertici di ciascuno dei quattro <a href="/wiki/Tetraedri" class="mw-redirect" title="Tetraedri">tetraedri</a> esterni, sono 4 degli 8 vertici del cubo stesso. Gli 8 vertici del cubo possono essere infatti suddivisi in due insiemi: nella descrizione con numeri binari, i vertici con somma delle coordinate pari </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 (0,0,0),(1,1,0),(1,0,1),(0,1,1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (0,0,0),(1,1,0),(1,0,1),(0,1,1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52e82888bd51b69848d0e9654932c342d546d810" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.56ex; height:2.843ex;" alt="{\displaystyle (0,0,0),(1,1,0),(1,0,1),(0,1,1)}" /></span></dd></dl> <p>ed i vertici con somma delle coordinate dispari </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 (1,0,0),(0,1,0),(0,0,1),(1,1,1).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (1,0,0),(0,1,0),(0,0,1),(1,1,1).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f960fdb0a99e0387fe493eed0299d5c980e1780" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:33.207ex; height:2.843ex;" alt="{\displaystyle (1,0,0),(0,1,0),(0,0,1),(1,1,1).}" /></span></dd></dl> <p>Ciascuna di queste quaterne individua un tetraedro, avente i vertici nella quaterna, ed i cui 6 spigoli sono diagonali delle 6 facce quadrate del cubo. </p> <div class="mw-heading mw-heading3"><h3 id="Cubi_in_un_dodecaedro">Cubi in un dodecaedro</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cubo&veaction=edit&section=8" title="Modifica la sezione Cubi in un dodecaedro" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cubo&action=edit&section=8" title="Edit section's source code: Cubi in un dodecaedro"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cube_to_dodecahedron_240px.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Cube_to_dodecahedron_240px.gif/220px-Cube_to_dodecahedron_240px.gif" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/5/58/Cube_to_dodecahedron_240px.gif 1.5x" data-file-width="240" data-file-height="240" /></a><figcaption>Applicazione di dodici pentagoni sugli spigoli di un cubo</figcaption></figure> <p>In modo analogo si vede che in un <a href="/wiki/Dodecaedro" title="Dodecaedro">dodecaedro</a> si possono inscrivere 5 cubi ciascuno dei quali ha gli spigoli che sono <a href="/wiki/Diametro" title="Diametro">diametri</a> di una faccia pentagonale del dodecaedro. Si osserva infatti che il dodecaedro ha 12 facce e che ogni faccia ha 5 diametri per un totale di 60 diametri superficiali, tutti della stessa lunghezza. Questi diametri si possono ripartire in 5 classi di 12 diametri ciascuna: i cinque diametri di una faccia sono assegnati a classi diverse e ogni classe è formata da diametri provenienti dalle 12 diverse facce. </p><p>Ciascuna di queste classi costituisce l'insieme degli spigoli di un cubo inscritto nel dodecaedro. Se si considera l'unione dei cinque cubi che si possono ottenere in questo modo da un dodecaedro dato, si ottiene un <a href="/wiki/Poliedro_composto" title="Poliedro composto">poliedro composto</a> regolare, detto <a href="/wiki/Cinque_cubi_nel_dodecaedro" title="Cinque cubi nel dodecaedro">cinque cubi nel dodecaedro</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Tassellazione_dello_spazio">Tassellazione dello spazio</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cubo&veaction=edit&section=9" title="Modifica la sezione Tassellazione dello spazio" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cubo&action=edit&section=9" title="Edit section's source code: Tassellazione dello spazio"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_0" poster="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Revolu%C3%A7%C3%A3o_de_um_cubo_%28IME-USP%29.webm/220px--Revolu%C3%A7%C3%A3o_de_um_cubo_%28IME-USP%29.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="124" data-durationhint="11" data-mwtitle="Revolução_de_um_cubo_(IME-USP).webm" data-mwprovider="wikimediacommons" resource="/wiki/File:Revolu%C3%A7%C3%A3o_de_um_cubo_(IME-USP).webm"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/f0/Revolu%C3%A7%C3%A3o_de_um_cubo_%28IME-USP%29.webm/Revolu%C3%A7%C3%A3o_de_um_cubo_%28IME-USP%29.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/f0/Revolu%C3%A7%C3%A3o_de_um_cubo_%28IME-USP%29.webm/Revolu%C3%A7%C3%A3o_de_um_cubo_%28IME-USP%29.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/f0/Revolu%C3%A7%C3%A3o_de_um_cubo_%28IME-USP%29.webm/Revolu%C3%A7%C3%A3o_de_um_cubo_%28IME-USP%29.webm.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/f/f0/Revolu%C3%A7%C3%A3o_de_um_cubo_%28IME-USP%29.webm" type="video/webm; codecs="vp8, vorbis"" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/f0/Revolu%C3%A7%C3%A3o_de_um_cubo_%28IME-USP%29.webm/Revolu%C3%A7%C3%A3o_de_um_cubo_%28IME-USP%29.webm.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="256" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/f0/Revolu%C3%A7%C3%A3o_de_um_cubo_%28IME-USP%29.webm/Revolu%C3%A7%C3%A3o_de_um_cubo_%28IME-USP%29.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/f0/Revolu%C3%A7%C3%A3o_de_um_cubo_%28IME-USP%29.webm/Revolu%C3%A7%C3%A3o_de_um_cubo_%28IME-USP%29.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/f0/Revolu%C3%A7%C3%A3o_de_um_cubo_%28IME-USP%29.webm/Revolu%C3%A7%C3%A3o_de_um_cubo_%28IME-USP%29.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span><figcaption>Rivoluzione del cubo intorno ad un asse</figcaption></figure> <p>Il cubo è il solo tra i <a href="/wiki/Solidi_platonici" class="mw-redirect" title="Solidi platonici">solidi platonici</a> che, con sue repliche, è in grado di riempire lo spazio con regolarità, cioè di fornire una <a href="/wiki/Tassellazione_dello_spazio" title="Tassellazione dello spazio">tassellazione dello spazio</a>. Godono della stessa proprietà anche i due <a href="/wiki/Solido_semiregolare" class="mw-redirect" title="Solido semiregolare">solidi semiregolari</a>, della stessa famiglia del cubo, il <a href="/w/index.php?title=Prisma_triangolare_regolare&action=edit&redlink=1" class="new" title="Prisma triangolare regolare (la pagina non esiste)">prisma triangolare regolare</a> ed il <a href="/w/index.php?title=Prisma_esagonale_regolare&action=edit&redlink=1" class="new" title="Prisma esagonale regolare (la pagina non esiste)">prisma esagonale regolare</a>, nonché il <a href="/wiki/Solido_archimedeo" title="Solido archimedeo">solido archimedeo</a> detto <a href="/wiki/Dodecaedro_rombico" title="Dodecaedro rombico">dodecaedro rombico</a>. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Stone_Dice_17.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Stone_Dice_17.JPG/220px-Stone_Dice_17.JPG" decoding="async" width="220" height="125" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Stone_Dice_17.JPG/330px-Stone_Dice_17.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/31/Stone_Dice_17.JPG/440px-Stone_Dice_17.JPG 2x" data-file-width="500" data-file-height="285" /></a><figcaption>I <a href="/wiki/Dado_(gioco)" title="Dado (gioco)">dadi da gioco</a> sono dei cubi.</figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="Altro">Altro</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cubo&veaction=edit&section=10" title="Modifica la sezione Altro" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cubo&action=edit&section=10" title="Edit section's source code: Altro"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>I comuni <a href="/wiki/Dado_(gioco)" title="Dado (gioco)">dadi da gioco</a> a sei facce hanno forma cubica. </p><p>Costruendo un modello materiale di cubo che ha ogni spigolo costituito da un <a href="/wiki/Resistore" title="Resistore">resistore</a> da 1 <a href="/wiki/Ohm" title="Ohm">ohm</a>, la resistenza tra due vertici adiacenti è di 7/12 Ω, quella tra due vertici opposti di 5/6 Ω. </p><p>L'<a href="/wiki/Ipercubo" title="Ipercubo">ipercubo</a> o cubo <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" /></span>-dimensionale è una generalizzazione del cubo in dimensione <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" /></span> arbitraria. </p> <div class="mw-heading mw-heading2"><h2 id="Voci_correlate">Voci correlate</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cubo&veaction=edit&section=11" title="Modifica la sezione Voci correlate" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cubo&action=edit&section=11" title="Edit section's source code: Voci correlate"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Cubo_di_Rubik" title="Cubo di Rubik">Cubo di Rubik</a></li> <li><a href="/wiki/Dado_da_gioco" class="mw-redirect" title="Dado da gioco">Dado da gioco</a></li> <li><a href="/wiki/Ipercubo" title="Ipercubo">Ipercubo</a></li> <li><a href="/wiki/Reticolo_booleano" class="mw-redirect" title="Reticolo booleano">Reticolo booleano</a></li> <li><a href="/wiki/Cubo_unitario" title="Cubo unitario">Cubo unitario</a></li> <li><a href="/wiki/Teorema_delle_intersezioni_dimensionali" title="Teorema delle intersezioni dimensionali">Teorema delle intersezioni dimensionali</a></li> <li><a href="/wiki/Sezioni_ipercubiche_ortoassiali" title="Sezioni ipercubiche ortoassiali">Sezioni ipercubiche ortoassiali</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Altri_progetti">Altri progetti</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cubo&veaction=edit&section=12" title="Modifica la sezione Altri progetti" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cubo&action=edit&section=12" title="Edit section's source code: Altri progetti"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <div id="interProject" class="toccolours" style="display: none; clear: both; margin-top: 2em"><p id="sisterProjects" style="background-color: #efefef; color: black; font-weight: bold; margin: 0"><span>Altri progetti</span></p><ul title="Collegamenti verso gli altri progetti Wikimedia"> <li class="" title=""><a href="https://it.wikiquote.org/wiki/Cubo" class="extiw" title="q:Cubo">Wikiquote</a></li> <li class="" title=""><a href="https://it.wiktionary.org/wiki/cubo" class="extiw" title="wikt:cubo">Wikizionario</a></li> <li class="" title=""><span class="plainlinks" title="commons:Category:Cube"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Cube?uselang=it">Wikimedia Commons</a></span></li></ul></div> <ul><li><span typeof="mw:File"><a href="https://it.wikiquote.org/wiki/" title="Collabora a Wikiquote"><img alt="Collabora a Wikiquote" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/18px-Wikiquote-logo.svg.png" decoding="async" width="18" height="21" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/27px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/36px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></a></span> <a href="https://it.wikiquote.org/wiki/" class="extiw" title="q:">Wikiquote</a> contiene citazioni sul <b><a href="https://it.wikiquote.org/wiki/Cubo" class="extiw" title="q:Cubo">cubo</a></b></li> <li><span typeof="mw:File"><a href="https://it.wiktionary.org/wiki/" title="Collabora a Wikizionario"><img alt="Collabora a Wikizionario" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wiktionary_small.svg/20px-Wiktionary_small.svg.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wiktionary_small.svg/40px-Wiktionary_small.svg.png 1.5x" data-file-width="350" data-file-height="350" /></a></span> <a href="https://it.wiktionary.org/wiki/" class="extiw" title="wikt:">Wikizionario</a> contiene il lemma di dizionario «<b><a href="https://it.wiktionary.org/wiki/cubo" class="extiw" title="wikt:cubo">cubo</a></b>»</li> <li><span typeof="mw:File"><a href="https://commons.wikimedia.org/wiki/?uselang=it" title="Collabora a Wikimedia Commons"><img alt="Collabora a Wikimedia Commons" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png" decoding="async" width="18" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png 1.5x" data-file-width="1024" data-file-height="1376" /></a></span> <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/?uselang=it">Wikimedia Commons</a></span> contiene immagini o altri file sul <b><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Cube?uselang=it">cubo</a></span></b></li></ul> <div class="mw-heading mw-heading2"><h2 id="Collegamenti_esterni">Collegamenti esterni</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cubo&veaction=edit&section=13" title="Modifica la sezione Collegamenti esterni" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cubo&action=edit&section=13" title="Edit section's source code: Collegamenti esterni"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li class="mw-empty-elt"></li> <li><cite id="CITEREFTreccani.it" class="citation web" style="font-style:normal"> <a rel="nofollow" class="external text" href="https://www.treccani.it/enciclopedia/cubo"><span style="font-style:italic;">cubo</span></a>, su <span style="font-style:italic;">Treccani.it – Enciclopedie on line</span>, <a href="/wiki/Istituto_dell%27Enciclopedia_Italiana" title="Istituto dell'Enciclopedia Italiana">Istituto dell'Enciclopedia Italiana</a>.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q812880#P3365" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite id="CITEREFEnciclopedia_Italiana" class="citation libro" style="font-style:normal"> <a href="/wiki/Arturo_Maroni" title="Arturo Maroni">Arturo Maroni</a>, <a rel="nofollow" class="external text" href="https://www.treccani.it/enciclopedia/cubo_(Enciclopedia-Italiana)/"><span style="font-style:italic;">CUBO</span></a>, in <span style="font-style:italic;"><a href="/wiki/Enciclopedia_Treccani" title="Enciclopedia Treccani">Enciclopedia Italiana</a></span>, <a href="/wiki/Istituto_dell%27Enciclopedia_Italiana" title="Istituto dell'Enciclopedia Italiana">Istituto dell'Enciclopedia Italiana</a>, 1931.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q812880#P4223" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite id="CITEREFDizionario_delle_scienze_fisiche" class="citation libro" style="font-style:normal"> <a rel="nofollow" class="external text" href="https://www.treccani.it/enciclopedia/cubo_(Dizionario-delle-Scienze-Fisiche)/"><span style="font-style:italic;">Cubo</span></a>, in <span style="font-style:italic;">Dizionario delle scienze fisiche</span>, <a href="/wiki/Istituto_dell%27Enciclopedia_Italiana" title="Istituto dell'Enciclopedia Italiana">Istituto dell'Enciclopedia Italiana</a>, 1996.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q812880#P10017" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite id="CITEREFVocabolario_Treccani" class="citation web" style="font-style:normal"> <a rel="nofollow" class="external text" href="https://www.treccani.it/vocabolario/cubo"><span style="font-style:italic;">Cubo</span></a>, su <span style="font-style:italic;"><a href="/wiki/Vocabolario_Treccani" title="Vocabolario Treccani">Vocabolario Treccani</a></span>, <a href="/wiki/Istituto_dell%27Enciclopedia_Italiana" title="Istituto dell'Enciclopedia Italiana">Istituto dell'Enciclopedia Italiana</a>.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q812880#P5844" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite id="CITEREFSapere.it" class="citation web" style="font-style:normal"> <a rel="nofollow" class="external text" href="https://www.sapere.it/enciclopedia/cubo.html"><span style="font-style:italic;">cubo</span></a>, su <span style="font-style:italic;">sapere.it</span>, <a href="/wiki/De_Agostini" title="De Agostini">De Agostini</a>.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q812880#P6706" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite id="CITEREFEnciclopedia_della_Matematica" class="citation libro" style="font-style:normal"> <a rel="nofollow" class="external text" href="https://www.treccani.it/enciclopedia/cubo_(Enciclopedia-della-Matematica)/"><span style="font-style:italic;">Cubo</span></a>, in <span style="font-style:italic;">Enciclopedia della Matematica</span>, <a href="/wiki/Istituto_dell%27Enciclopedia_Italiana" title="Istituto dell'Enciclopedia Italiana">Istituto dell'Enciclopedia Italiana</a>, 2013.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q812880#P9621" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite id="CITEREFBritannica.com" class="citation web" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) <a rel="nofollow" class="external text" href="https://www.britannica.com/topic/cube-mathematics"><span style="font-style:italic;">cube</span></a>, su <span style="font-style:italic;"><a href="/wiki/Enciclopedia_Britannica" title="Enciclopedia Britannica">Enciclopedia Britannica</a></span>, Encyclopædia Britannica, Inc.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q812880#P1417" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite id="CITEREFOpen_Library" class="citation web" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) <a rel="nofollow" class="external text" href="https://openlibrary.org/subjects/cube"><span style="font-style:italic;">Opere riguardanti Cube</span></a>, su <span style="font-style:italic;"><a href="/wiki/Open_Library" class="mw-redirect" title="Open Library">Open Library</a></span>, <a href="/wiki/Internet_Archive" title="Internet Archive">Internet Archive</a>.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q812880#P3847" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite id="CITEREFMathWorld" class="citation web" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) Eric W. Weisstein, <a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/Cube.html"><span style="font-style:italic;">Cube</span></a>, su <span style="font-style:italic;"><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></span>, Wolfram Research.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q812880#P2812" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite id="CITEREFSpringerEOM" class="citation web" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) <a rel="nofollow" class="external text" href="https://encyclopediaofmath.org/wiki/Cube"><span style="font-style:italic;">Cube</span></a>, su <span style="font-style:italic;"><a href="/wiki/Encyclopaedia_of_Mathematics" title="Encyclopaedia of Mathematics">Encyclopaedia of Mathematics</a></span>, Springer e European Mathematical Society.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q812880#P7554" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" data-file-width="600" data-file-height="600" /></a></span></li></ul> <style data-mw-deduplicate="TemplateStyles:r141815314">.mw-parser-output .navbox{border:1px solid #aaa;clear:both;margin:auto;padding:2px;width:100%}.mw-parser-output .navbox th{padding-left:1em;padding-right:1em;text-align:center}.mw-parser-output .navbox>tbody>tr:first-child>th{background:#ccf;font-size:90%;width:100%;color:var(--color-base,black)}.mw-parser-output .navbox_navbar{float:left;margin:0;padding:0 10px 0 0;text-align:left;width:6em}.mw-parser-output .navbox_title{font-size:110%}.mw-parser-output .navbox_abovebelow{background:#ddf;font-size:90%;font-weight:normal}.mw-parser-output .navbox_group{background:#ddf;font-size:90%;padding:0 10px;white-space:nowrap}.mw-parser-output .navbox_list{font-size:90%;width:100%}.mw-parser-output .navbox_list a{white-space:nowrap}html:not(.vector-feature-night-mode-enabled) .mw-parser-output .navbox_odd{background:#fdfdfd;color:var(--color-base,black)}html:not(.vector-feature-night-mode-enabled) .mw-parser-output .navbox_even{background:#f7f7f7;color:var(--color-base,black)}.mw-parser-output .navbox a.mw-selflink{color:var(--color-base,black)}.mw-parser-output .navbox_center{text-align:center}.mw-parser-output .navbox .navbox_image{padding-left:7px;vertical-align:middle;width:0}.mw-parser-output .navbox+.navbox{margin-top:-1px}.mw-parser-output .navbox .mw-collapsible-toggle{font-weight:normal;text-align:right;width:7em}body.skin--responsive .mw-parser-output .navbox_image img{max-width:none!important}.mw-parser-output .subnavbox{margin:-3px;width:100%}.mw-parser-output .subnavbox_group{background:#e6e6ff;padding:0 10px}@media screen{html.skin-theme-clientpref-night .mw-parser-output .navbox>tbody>tr:first-child>th{background:var(--background-color-interactive)!important}html.skin-theme-clientpref-night .mw-parser-output .navbox th{color:var(--color-base)!important}html.skin-theme-clientpref-night .mw-parser-output .navbox_abovebelow,html.skin-theme-clientpref-night .mw-parser-output .navbox_group{background:var(--background-color-interactive-subtle)!important}html.skin-theme-clientpref-night .mw-parser-output .subnavbox_group{background:var(--background-color-neutral-subtle)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbox>tbody>tr:first-child>th{background:var(--background-color-interactive)!important}html.skin-theme-clientpref-os .mw-parser-output .navbox th{color:var(--color-base)!important}html.skin-theme-clientpref-os .mw-parser-output .navbox_abovebelow,html.skin-theme-clientpref-os .mw-parser-output .navbox_group{background:var(--background-color-interactive-subtle)!important}html.skin-theme-clientpref-os .mw-parser-output .subnavbox_group{background:var(--background-color-neutral-subtle)!important}}</style><table class="navbox mw-collapsible autocollapse noprint metadata" id="navbox-Poliedri"><tbody><tr><th colspan="2"><div class="navbox_navbar"><div class="noprint plainlinks" style="background-color:transparent; padding:0; font-size:xx-small; color:var(--color-base, #000000); white-space:nowrap;"><a href="/wiki/Template:Poliedri" title="Template:Poliedri"><span title="Vai alla pagina del template">V</span></a> · <a href="/wiki/Discussioni_template:Poliedri" title="Discussioni template:Poliedri"><span title="Discuti del template">D</span></a> · <a class="external text" href="https://it.wikipedia.org/w/index.php?title=Template:Poliedri&action=edit"><span title="Modifica il template. Usa l'anteprima prima di salvare">M</span></a></div></div><span class="navbox_title">I <a href="/wiki/Poliedro" title="Poliedro">poliedri</a></span></th></tr><tr><th colspan="1" class="navbox_group"><a href="/wiki/Poliedro_uniforme" title="Poliedro uniforme">Poliedri uniformi</a></th><td colspan="1" class="navbox_list navbox_odd"><table class="subnavbox"><tbody><tr><th class="subnavbox_group"><a href="/wiki/Solido_platonico" title="Solido platonico">Solidi platonici</a> (regolari)</th><td colspan="1"><a href="/wiki/Tetraedro" title="Tetraedro">Tetraedro</a><b> ·</b> <a class="mw-selflink selflink">Cubo</a><b> ·</b> <a href="/wiki/Ottaedro" title="Ottaedro">Ottaedro</a><b> ·</b> <a href="/wiki/Dodecaedro" title="Dodecaedro">Dodecaedro</a><b> ·</b> <a href="/wiki/Icosaedro" title="Icosaedro">Icosaedro</a></td></tr><tr><th class="subnavbox_group"><a href="/wiki/Solido_archimedeo" title="Solido archimedeo">Solidi archimedei</a><br />(semiregolari)</th><td colspan="1"><a href="/wiki/Tetraedro_troncato" title="Tetraedro troncato">Tetraedro troncato</a><b> ·</b> <a href="/wiki/Cubottaedro" title="Cubottaedro">Cubottaedro</a><b> ·</b> <a href="/wiki/Cubo_troncato" title="Cubo troncato">Cubo troncato</a><b> ·</b> <a href="/wiki/Ottaedro_troncato" title="Ottaedro troncato">Ottaedro troncato</a><b> ·</b> <a href="/wiki/Rombicubottaedro" title="Rombicubottaedro">Rombicubottaedro</a><b> ·</b> <a href="/wiki/Cubottaedro_troncato" title="Cubottaedro troncato">Cubottaedro troncato</a><b> ·</b> <a href="/wiki/Cubo_simo" title="Cubo simo">Cubo simo</a><b> ·</b> <a href="/wiki/Icosidodecaedro" title="Icosidodecaedro">Icosidodecaedro</a><b> ·</b> <a href="/wiki/Dodecaedro_troncato" title="Dodecaedro troncato">Dodecaedro troncato</a><b> ·</b> <a href="/wiki/Icosaedro_troncato" title="Icosaedro troncato">Icosaedro troncato</a><b> ·</b> <a href="/wiki/Rombicosidodecaedro" title="Rombicosidodecaedro">Rombicosidodecaedro</a><b> ·</b> <a href="/wiki/Icosidodecaedro_troncato" title="Icosidodecaedro troncato">Icosidodecaedro troncato</a><b> ·</b> <a href="/wiki/Dodecaedro_simo" title="Dodecaedro simo">Dodecaedro simo</a></td></tr><tr><th class="subnavbox_group"><a href="/wiki/Poliedro_di_Keplero-Poinsot" title="Poliedro di Keplero-Poinsot">Solidi di Keplero-Poinsot</a></th><td colspan="1"><a href="/wiki/Grande_dodecaedro" title="Grande dodecaedro">Grande dodecaedro</a><b> ·</b> <a href="/wiki/Piccolo_dodecaedro_stellato" title="Piccolo dodecaedro stellato">Piccolo dodecaedro stellato</a><b> ·</b> <a href="/wiki/Grande_dodecaedro_stellato" title="Grande dodecaedro stellato">Grande dodecaedro stellato</a><b> ·</b> <a href="/wiki/Grande_icosaedro" title="Grande icosaedro">Grande icosaedro</a></td></tr><tr><th class="subnavbox_group">Altri</th><td colspan="1"><a href="/wiki/Prisma" title="Prisma">Prismi</a><b> ·</b> <a href="/wiki/Antiprisma" title="Antiprisma">Antiprismi</a><b> ·</b> <a href="/wiki/Poliedro_stellato_uniforme" title="Poliedro stellato uniforme">Poliedri stellati uniformi</a></td></tr></tbody></table></td></tr><tr><th colspan="1" class="navbox_group"><a href="/wiki/Solido_di_Catalan" title="Solido di Catalan">Solidi di Catalan</a><br />(semiregolari duali)</th><td colspan="1" class="navbox_list navbox_even"><a href="/wiki/Triacistetraedro" title="Triacistetraedro">Triacistetraedro</a><b> ·</b> <a href="/wiki/Dodecaedro_rombico" title="Dodecaedro rombico">Dodecaedro rombico</a><b> ·</b> <a href="/wiki/Triacisottaedro" title="Triacisottaedro">Triacisottaedro</a><b> ·</b> <a href="/wiki/Tetracisesaedro" title="Tetracisesaedro">Tetracisesaedro</a><b> ·</b> <a href="/wiki/Icositetraedro_trapezoidale" title="Icositetraedro trapezoidale">Icositetraedro trapezoidale</a><b> ·</b> <a href="/wiki/Esacisottaedro" title="Esacisottaedro">Esacisottaedro</a><b> ·</b> <a href="/wiki/Icositetraedro_pentagonale" title="Icositetraedro pentagonale">Icositetraedro pentagonale</a><b> ·</b> <a href="/wiki/Triacontaedro_rombico" title="Triacontaedro rombico">Triacontaedro rombico</a><b> ·</b> <a href="/wiki/Triacisicosaedro" title="Triacisicosaedro">Triacisicosaedro</a><b> ·</b> <a href="/wiki/Pentacisdodecaedro" title="Pentacisdodecaedro">Pentacisdodecaedro</a><b> ·</b> <a href="/wiki/Esacontaedro_trapezoidale" title="Esacontaedro trapezoidale">Esacontaedro trapezoidale</a><b> ·</b> <a href="/wiki/Esacisicosaedro" title="Esacisicosaedro">Esacisicosaedro</a><b> ·</b> <a href="/wiki/Esacontaedro_pentagonale" title="Esacontaedro pentagonale">Esacontaedro pentagonale</a></td></tr><tr><th colspan="1" class="navbox_group">Altri</th><td colspan="1" class="navbox_list navbox_odd"><a href="/wiki/Bipiramide" title="Bipiramide">Bipiramidi</a><b> ·</b> <a href="/wiki/Trapezoedro" title="Trapezoedro">Trapezoedri</a><b> ·</b> <a href="/wiki/Piramide_(geometria)" title="Piramide (geometria)">Piramidi</a><b> ·</b> <a href="/wiki/Cupola_(geometria)" title="Cupola (geometria)">Cupola</a><b> ·</b> <a href="/wiki/Tronco_(geometria)" title="Tronco (geometria)">Tronco di piramide</a><b> ·</b> <a href="/wiki/Solido_di_Johnson" title="Solido di Johnson">Solidi di Johnson</a><b> ·</b> <a href="/wiki/Poliedro_di_Cs%C3%A1sz%C3%A1r" title="Poliedro di Császár">Poliedro di Császár</a><b> ·</b> <a href="/wiki/Poliedro_di_Szilassi" title="Poliedro di Szilassi">Poliedro di Szilassi</a><b> ·</b> <a href="/wiki/Scutoide" title="Scutoide">Scutoide</a></td></tr><tr><th colspan="2" class="navbox_abovebelow"><a href="/wiki/Poliedro_duale" title="Poliedro duale">Poliedro duale</a><b> ·</b> <a href="/wiki/Formula_di_Eulero_per_i_poliedri" title="Formula di Eulero per i poliedri">Formula di Eulero per i poliedri</a><b> ·</b> <a href="/wiki/Sviluppo_di_solidi" title="Sviluppo di solidi">Sviluppo di solidi</a></th></tr></tbody></table> <style data-mw-deduplicate="TemplateStyles:r140554510">.mw-parser-output .CdA{border:1px solid #aaa;width:100%;margin:auto;font-size:90%;padding:2px}.mw-parser-output .CdA th{background-color:#f2f2f2;font-weight:bold;width:20%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .CdA{border-color:#54595D}html.skin-theme-clientpref-night .mw-parser-output .CdA th{background-color:#202122}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .CdA{border-color:#54595D}html.skin-theme-clientpref-os .mw-parser-output .CdA th{background-color:#202122}}</style><table class="CdA"><tbody><tr><th><a href="/wiki/Aiuto:Controllo_di_autorit%C3%A0" title="Aiuto:Controllo di autorità">Controllo di autorità</a></th><td><a href="/wiki/Nuovo_soggettario" title="Nuovo soggettario">Thesaurus BNCF</a> <span class="uid"><a rel="nofollow" class="external text" href="https://thes.bncf.firenze.sbn.it/termine.php?id=19714">19714</a></span><span style="font-weight:bold;"> ·</span> <a href="/wiki/Library_of_Congress_Control_Number" title="Library of Congress Control Number">LCCN</a> <span class="uid">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) <a rel="nofollow" class="external text" href="http://id.loc.gov/authorities/subjects/sh85034644">sh85034644</a></span><span style="font-weight:bold;"> ·</span> <a href="/wiki/Gemeinsame_Normdatei" title="Gemeinsame Normdatei">GND</a> <span class="uid">(<span style="font-weight:bolder; font-size:80%"><abbr title="tedesco">DE</abbr></span>) <a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4079396-5">4079396-5</a></span><span style="font-weight:bold;"> ·</span> <a href="/wiki/Biblioteca_nazionale_di_Francia" title="Biblioteca nazionale di Francia">BNF</a> <span class="uid">(<span style="font-weight:bolder; font-size:80%"><abbr title="francese">FR</abbr></span>) <a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb11947058p">cb11947058p</a> <a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb11947058p">(data)</a></span><span style="font-weight:bold;"> ·</span> <a href="/wiki/Biblioteca_nazionale_di_Israele" title="Biblioteca nazionale di Israele">J9U</a> <span class="uid">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr>, <abbr title="ebraico">HE</abbr></span>) <a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007535952905171">987007535952905171</a></span></td></tr></tbody></table> <div class="noprint" style="width:100%; padding: 3px 0; display: flex; flex-wrap: wrap; row-gap: 4px; column-gap: 8px; box-sizing: border-box;"><div style="flex-grow: 1"><style data-mw-deduplicate="TemplateStyles:r140555418">.mw-parser-output .itwiki-template-occhiello{width:100%;line-height:25px;border:1px solid #CCF;background-color:#F0EEFF;box-sizing:border-box}.mw-parser-output .itwiki-template-occhiello-progetto{background-color:#FAFAFA}@media screen{html.skin-theme-clientpref-night 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