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<div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Páginas para editores desconectados <a href="/wiki/Ayuda:Introducci%C3%B3n" aria-label="Obtenga más información sobre editar"><span>más información</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Especial:MisContribuciones" title="Una lista de modificaciones hechas desde esta dirección IP [y]" accesskey="y"><span>Contribuciones</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Especial:MiDiscusi%C3%B3n" title="Discusión sobre ediciones hechas desde esta dirección IP [n]" accesskey="n"><span>Discusión</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div 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<ul id="toc-Enlaces_externos-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="Contenidos" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Cambiar a la tabla de contenidos" > <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">Cambiar a la tabla de contenidos</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">Esfera inscrita</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Ir a un artículo en otro idioma. Disponible en 16 idiomas" > <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-16" 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">16 idiomas</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%83%D8%B1%D8%A9_%D8%AF%D8%A7%D8%AE%D9%84%D9%8A%D8%A9" title="كرة داخلية (árabe)" lang="ar" hreflang="ar" data-title="كرة داخلية" data-language-autonym="العربية" data-language-local-name="árabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%92%D0%BF%D0%B8%D1%81%D0%B0%D0%BD%D0%B0_%D1%81%D1%84%D0%B5%D1%80%D0%B0" title="Вписана сфера (búlgaro)" lang="bg" hreflang="bg" data-title="Вписана сфера" data-language-autonym="Български" data-language-local-name="búlgaro" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A8%D0%B0%D0%BB_%D1%81%D1%84%D0%B5%D1%80%D0%B0" title="Шал сфера (chuvasio)" lang="cv" hreflang="cv" data-title="Шал сфера" data-language-autonym="Чӑвашла" data-language-local-name="chuvasio" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Inkugel" title="Inkugel (alemán)" lang="de" hreflang="de" data-title="Inkugel" data-language-autonym="Deutsch" data-language-local-name="alemán" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Inscribed_sphere" title="Inscribed sphere (inglés)" lang="en" hreflang="en" data-title="Inscribed sphere" data-language-autonym="English" data-language-local-name="inglés" 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/Enskribita_sfero" title="Enskribita sfero (esperanto)" lang="eo" hreflang="eo" data-title="Enskribita sfero" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Sph%C3%A8re_inscrite" title="Sphère inscrite (francés)" lang="fr" hreflang="fr" data-title="Sphère inscrite" data-language-autonym="Français" data-language-local-name="francés" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Esfera_inscrita" title="Esfera inscrita (gallego)" lang="gl" hreflang="gl" data-title="Esfera inscrita" data-language-autonym="Galego" data-language-local-name="gallego" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%86%D5%A5%D6%80%D5%A3%D5%AE%D5%A1%D5%AE_%D5%A3%D5%B6%D5%A4%D5%A1%D5%B5%D5%AB%D5%B6_%D5%B4%D5%A1%D5%AF%D5%A5%D6%80%D6%87%D5%B8%D6%82%D5%B5%D5%A9" title="Ներգծած գնդային մակերևույթ (armenio)" lang="hy" hreflang="hy" data-title="Ներգծած գնդային մակերևույթ" data-language-autonym="Հայերեն" data-language-local-name="armenio" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%86%85%E6%8E%A5%E7%90%83%E9%9D%A2" title="内接球面 (japonés)" lang="ja" hreflang="ja" data-title="内接球面" data-language-autonym="日本語" data-language-local-name="japonés" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Kula_wpisana" title="Kula wpisana (polaco)" lang="pl" hreflang="pl" data-title="Kula wpisana" data-language-autonym="Polski" data-language-local-name="polaco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Sfer%C4%83_%C3%AEnscris%C4%83" title="Sferă înscrisă (rumano)" lang="ro" hreflang="ro" data-title="Sferă înscrisă" data-language-autonym="Română" data-language-local-name="rumano" 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%92%D0%BF%D0%B8%D1%81%D0%B0%D0%BD%D0%BD%D0%B0%D1%8F_%D1%81%D1%84%D0%B5%D1%80%D0%B0" title="Вписанная сфера (ruso)" lang="ru" hreflang="ru" data-title="Вписанная сфера" data-language-autonym="Русский" data-language-local-name="ruso" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%89%E0%AE%9F%E0%AF%8D%E0%AE%95%E0%AF%8B%E0%AE%B3%E0%AE%AE%E0%AF%8D" title="உட்கோளம் (tamil)" lang="ta" hreflang="ta" data-title="உட்கோளம்" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%92%D0%BF%D0%B8%D1%81%D0%B0%D0%BD%D0%B0_%D1%81%D1%84%D0%B5%D1%80%D0%B0" title="Вписана сфера (ucraniano)" lang="uk" hreflang="uk" data-title="Вписана сфера" data-language-autonym="Українська" data-language-local-name="ucraniano" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%86%85%E5%88%87%E7%90%83" title="内切球 (chino)" lang="zh" hreflang="zh" data-title="内切球" data-language-autonym="中文" data-language-local-name="chino" class="interlanguage-link-target"><span>中文</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/Q683362#sitelinks-wikipedia" title="Editar enlaces interlingüísticos" class="wbc-editpage">Editar enlaces</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="Espacios de nombres"> <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/Esfera_inscrita" title="Ver la página de contenido [c]" accesskey="c"><span>Artículo</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Discusi%C3%B3n:Esfera_inscrita&action=edit&redlink=1" rel="discussion" class="new" title="Discusión acerca de la página (aún no redactado) [t]" accesskey="t"><span>Discusión</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="Cambiar variante de idioma" > <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">español</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="Vistas"> <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/Esfera_inscrita"><span>Leer</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Esfera_inscrita&action=edit" title="Editar esta página [e]" accesskey="e"><span>Editar</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Esfera_inscrita&action=history" title="Versiones anteriores de esta página [h]" accesskey="h"><span>Ver historial</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Página de herramientas"> <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="Herramientas" > <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">Herramientas</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">Herramientas</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">mover a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">ocultar</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Más opciones" > <div class="vector-menu-heading"> Acciones </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/Esfera_inscrita"><span>Leer</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Esfera_inscrita&action=edit" title="Editar esta página [e]" accesskey="e"><span>Editar</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Esfera_inscrita&action=history"><span>Ver historial</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Especial:LoQueEnlazaAqu%C3%AD/Esfera_inscrita" title="Lista de todas las páginas de la wiki que enlazan aquí [j]" accesskey="j"><span>Lo que enlaza aquí</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Especial:CambiosEnEnlazadas/Esfera_inscrita" rel="nofollow" title="Cambios recientes en las páginas que enlazan con esta [k]" accesskey="k"><span>Cambios en enlazadas</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=es" title="Subir archivos [u]" accesskey="u"><span>Subir archivo</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Especial:P%C3%A1ginasEspeciales" title="Lista de todas las páginas especiales [q]" accesskey="q"><span>Páginas especiales</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Esfera_inscrita&oldid=154465190" title="Enlace permanente a esta versión de la página"><span>Enlace permanente</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Esfera_inscrita&action=info" title="Más información sobre esta página"><span>Información de la página</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Especial:Citar&page=Esfera_inscrita&id=154465190&wpFormIdentifier=titleform" title="Información sobre cómo citar esta página"><span>Citar esta página</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Especial:Acortador_de_URL&url=https%3A%2F%2Fes.wikipedia.org%2Fwiki%2FEsfera_inscrita"><span>Obtener URL acortado</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Especial:QrCode&url=https%3A%2F%2Fes.wikipedia.org%2Fwiki%2FEsfera_inscrita"><span>Descargar código 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"> Imprimir/exportar </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=Especial:Libro&bookcmd=book_creator&referer=Esfera+inscrita"><span>Crear un libro</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Especial:DownloadAsPdf&page=Esfera_inscrita&action=show-download-screen"><span>Descargar como PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Esfera_inscrita&printable=yes" title="Versión imprimible de esta página [p]" accesskey="p"><span>Versión para imprimir</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"> En otros proyectos </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:Inscribed_spheres" hreflang="en"><span>Wikimedia Commons</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/Q683362" title="Enlace al elemento conectado del repositorio de datos [g]" accesskey="g"><span>Elemento de 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="Página de herramientas"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Apariencia"> <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">Apariencia</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mover a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ocultar</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">De Wikipedia, la enciclopedia libre</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="es" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Archivo:01_Tetraeder-Gr%C3%B6%C3%9Fen.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/01_Tetraeder-Gr%C3%B6%C3%9Fen.png/220px-01_Tetraeder-Gr%C3%B6%C3%9Fen.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/01_Tetraeder-Gr%C3%B6%C3%9Fen.png/330px-01_Tetraeder-Gr%C3%B6%C3%9Fen.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/98/01_Tetraeder-Gr%C3%B6%C3%9Fen.png/440px-01_Tetraeder-Gr%C3%B6%C3%9Fen.png 2x" data-file-width="929" data-file-height="931" /></a><figcaption><a href="/wiki/Tetraedro" title="Tetraedro">Tetraedro</a> con la insfera en rojo (también la semiesfera en verde, la circunsfera en azul)</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Archivo:Kepler-solar-system-1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/Kepler-solar-system-1.png/220px-Kepler-solar-system-1.png" decoding="async" width="220" height="242" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/Kepler-solar-system-1.png/330px-Kepler-solar-system-1.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/19/Kepler-solar-system-1.png/440px-Kepler-solar-system-1.png 2x" data-file-width="704" data-file-height="774" /></a><figcaption>En su libro de 1597 <i><a href="/wiki/Mysterium_Cosmographicum" title="Mysterium Cosmographicum">Mysterium Cosmographicum</a></i>, <a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Kepler</a> modeló el <a href="/wiki/Sistema_Solar" class="mw-redirect" title="Sistema Solar">Sistema Solar</a> con sus entonces conocidas órbitas de seis planetas mediante <a href="/wiki/S%C3%B3lidos_plat%C3%B3nicos" title="Sólidos platónicos">sólidos platónicos</a> anidados, cada uno circunscrito e inscrito por una esfera.</figcaption></figure> <p>En <a href="/wiki/Geometr%C3%ADa" title="Geometría">geometría</a>, la <b>esfera inscrita</b> o <b>insfera</b> de un <a href="/wiki/Poliedro_convexo" title="Poliedro convexo">poliedro convexo</a> es una <a href="/wiki/Esfera" title="Esfera">esfera</a> contenida en el poliedro y <a href="/wiki/Tangente_(geometr%C3%ADa)" title="Tangente (geometría)"> tangente</a> a cada una de sus caras. Es la mayor esfera contenida íntegramente en el poliedro, y es <a href="/wiki/Dualidad_(matem%C3%A1ticas)" class="mw-redirect" title="Dualidad (matemáticas)">dual</a> a la <a href="/w/index.php?title=Circunsfera&action=edit&redlink=1" class="new" title="Circunsfera (aún no redactado)">circunsfera</a> del <a href="/wiki/Poliedro_dual" class="mw-redirect" title="Poliedro dual">poliedro dual</a>. </p><p>El radio de la esfera inscrita en un poliedro <i>P</i> se llama <b>inradio</b> de <i>P</i>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Interpretaciones">Interpretaciones</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera_inscrita&action=edit&section=1" title="Editar sección: Interpretaciones"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Todos los <a href="/wiki/Poliedro_regular" title="Poliedro regular"> poliedros regulares</a> tienen esferas inscritas, pero la mayoría de los poliedros irregulares no tienen todas las facetas tangentes a una esfera común, aunque todavía es posible definir la esfera contenida más grande para tales formas. Para tales casos, la noción de una <b>insfera</b> no parece haber sido definida correctamente y se encuentran varias interpretaciones de una <b>insfera</b>: </p> <ul><li>La esfera tangente a todas las caras (si existe).</li> <li>La esfera tangente a todos los planos de las caras (si existe).</li> <li>La esfera tangente a un conjunto dado de caras (si existe).</li> <li>La esfera más grande que puede caber dentro del poliedro.</li></ul> <p>A menudo estas esferas coinciden, lo que lleva a confusión sobre qué propiedades definen exactamente la insfera para los poliedros en los que no coinciden. </p><p>Por ejemplo, el <a href="/wiki/Peque%C3%B1o_dodecaedro_estrellado" title="Pequeño dodecaedro estrellado">pequeño dodecaedro estrellado</a> regular tiene una esfera tangente a todas las caras, mientras que una esfera mayor puede caber dentro del poliedro. ¿Cuál es la insfera? Autoridades importantes como Coxeter<sup id="cite_ref-1" class="reference separada"><a href="#cite_note-1"><span class="corchete-llamada">[</span>1<span class="corchete-llamada">]</span></a></sup> o Cundy & Rollett<sup id="cite_ref-2" class="reference separada"><a href="#cite_note-2"><span class="corchete-llamada">[</span>2<span class="corchete-llamada">]</span></a></sup> tienen bastante claro que la esfera tangente a las caras es la insfera. De nuevo, estas autoridades están de acuerdo en que los poliedros <a href="/wiki/S%C3%B3lidos_arquimedianos" title="Sólidos arquimedianos">arquimedianos</a> (con caras regulares y vértices equivalentes) no tienen insferas, mientras que los poliedros duales arquimedianos o <a href="/wiki/S%C3%B3lidos_de_Catalan" title="Sólidos de Catalan">sólidos de Catalan</a> sí tienen insferas. Pero muchos autores no respetan estas distinciones y asumen otras definiciones para las "esferas de inspiración" de sus poliedros. </p> <div class="mw-heading mw-heading2"><h2 id="Véase_también"><span id="V.C3.A9ase_tambi.C3.A9n"></span>Véase también</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera_inscrita&action=edit&section=2" title="Editar sección: Véase también"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Esfera_circunscrita" title="Esfera circunscrita">Esfera circunscrita</a></li> <li><a href="/wiki/Circunferencia_inscrita_y_exinscrita_en_un_tri%C3%A1ngulo" title="Circunferencia inscrita y exinscrita en un triángulo">Circunferencia inscrita y exinscrita en un triángulo</a></li> <li><a href="/wiki/Interesfera" title="Interesfera">Interesfera</a></li> <li><a href="/wiki/Empaquetamiento_de_esferas" title="Empaquetamiento de esferas">Empaquetamiento de esferas</a></li> <li><a href="/wiki/S%C3%B3lidos_de_Catalan" title="Sólidos de Catalan">Sólidos de Catalan</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Referencias">Referencias</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera_inscrita&action=edit&section=3" title="Editar sección: Referencias"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="listaref" style="list-style-type: decimal;"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><span style="color:var(--color-subtle,#555);">(en inglés)</span> Coxeter, H.S.M. <i>Regular Polytopes</i> 3rd Edn. Dover, 1973</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><span style="color:var(--color-subtle,#555);">(en inglés)</span> Cundy, H.M., Rollett, A.P. <i>Mathematical Models</i>, 2nd Edn. OUP, 1961</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografía"><span id="Bibliograf.C3.ADa"></span>Bibliografía</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera_inscrita&action=edit&section=4" title="Editar sección: Bibliografía"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Coxeter, H.S.M. <i><a href="/w/index.php?title=Regular_Polytopes_(book)&action=edit&redlink=1" class="new" title="Regular Polytopes (book) (aún no redactado)">Regular Polytopes</a></i> 3rd Edn. Dover (1973).</li> <li>Cundy, H.M. and Rollett, A.P. <i><a href="/w/index.php?title=Mathematical_Models_(Cundy_and_Rollett)&action=edit&redlink=1" class="new" title="Mathematical Models (Cundy and Rollett) (aún no redactado)">Mathematical Models</a></i>, 2nd Edn. OUP (1961).</li></ul> <div class="mw-heading mw-heading2"><h2 id="Enlaces_externos">Enlaces externos</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera_inscrita&action=edit&section=5" title="Editar sección: Enlaces externos"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span id="Reference-Mathworld-Insphere" class="citation web"><a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W</a>. <a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/Insphere.html">«Insphere»</a>. En Weisstein, Eric W, ed. <i><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></i> <span style="color:var(--color-subtle, #555 );">(en inglés)</span>. <a href="/wiki/Wolfram_Research" title="Wolfram Research">Wolfram Research</a>.</span><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fes.wikipedia.org%3AEsfera+inscrita&rft.atitle=Insphere&rft.au=Weisstein%2C+Eric+W&rft.aulast=Weisstein%2C+Eric+W&rft.genre=article&rft.jtitle=MathWorld&rft.pub=Wolfram+Research&rft_id=http%3A%2F%2Fmathworld.wolfram.com%2FInsphere.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Obtenido de «<a dir="ltr" href="https://es.wikipedia.org/w/index.php?title=Esfera_inscrita&oldid=154465190">https://es.wikipedia.org/w/index.php?title=Esfera_inscrita&oldid=154465190</a>»</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Especial:Categor%C3%ADas" title="Especial:Categorías">Categorías</a>: <ul><li><a href="/wiki/Categor%C3%ADa:Geometr%C3%ADa_elemental" title="Categoría:Geometría elemental">Geometría elemental</a></li><li><a href="/wiki/Categor%C3%ADa:Poliedros" title="Categoría:Poliedros">Poliedros</a></li><li><a href="/wiki/Categor%C3%ADa:Esferas" title="Categoría:Esferas">Esferas</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Esta página se editó por última vez el 9 oct 2023 a las 14:15.</li> <li id="footer-info-copyright">El texto está disponible bajo la <a href="/wiki/Wikipedia:Texto_de_la_Licencia_Creative_Commons_Atribuci%C3%B3n-CompartirIgual_4.0_Internacional" title="Wikipedia:Texto de la Licencia Creative Commons Atribución-CompartirIgual 4.0 Internacional">Licencia Creative Commons Atribución-CompartirIgual 4.0</a>; pueden aplicarse cláusulas adicionales. 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