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Ortoedro - Wikipedia, la enciclopedia libre
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lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ocultar</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Inicio</div> </a> </li> <li id="toc-Fórmulas_del_ortoedro" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Fórmulas_del_ortoedro"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Fórmulas del ortoedro</span> </div> </a> <button aria-controls="toc-Fórmulas_del_ortoedro-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Alternar subsección Fórmulas del ortoedro</span> </button> <ul id="toc-Fórmulas_del_ortoedro-sublist" class="vector-toc-list"> <li id="toc-Áreas" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Áreas"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Áreas</span> </div> </a> <ul id="toc-Áreas-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Volumen" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Volumen"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Volumen</span> </div> </a> <ul id="toc-Volumen-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Diagonal" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Diagonal"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Diagonal</span> </div> </a> <ul id="toc-Diagonal-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Notas_y_referencias" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notas_y_referencias"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Notas y referencias</span> </div> </a> <ul id="toc-Notas_y_referencias-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Véase_también" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Véase_también"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Véase también</span> </div> </a> <ul id="toc-Véase_también-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Enlaces_externos" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Enlaces_externos"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Enlaces externos</span> </div> </a> <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" title="Tabla de contenidos" > <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">Ortoedro</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 56 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-56" 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">56 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%85%D8%AA%D9%88%D8%A7%D8%B2%D9%8A_%D9%85%D8%B3%D8%AA%D8%B7%D9%8A%D9%84%D8%A7%D8%AA" title="متوازي مستطيلات – árabe" lang="ar" hreflang="ar" data-title="متوازي مستطيلات" data-language-autonym="العربية" data-language-local-name="árabe" 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%D8%AA%D9%88%D8%A7%D8%B2%D9%8A_%D9%84%D9%85%D8%B3%D8%AA%D8%B7%D9%8A%D9%84%D8%A7%D8%AA" title="متوازي لمستطيلات – Moroccan Arabic" lang="ary" hreflang="ary" data-title="متوازي لمستطيلات" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/D%C3%BCzbucaql%C4%B1_paralelepiped" title="Düzbucaqlı paralelepiped – azerbaiyano" lang="az" hreflang="az" data-title="Düzbucaqlı paralelepiped" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaiyano" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D1%80%D0%B0%D0%B2%D0%BE%D1%8A%D0%B3%D1%8A%D0%BB%D0%B5%D0%BD_%D0%BF%D0%B0%D1%80%D0%B0%D0%BB%D0%B5%D0%BB%D0%B5%D0%BF%D0%B8%D0%BF%D0%B5%D0%B4" title="Правоъгълен паралелепипед – búlgaro" lang="bg" hreflang="bg" data-title="Правоъгълен паралелепипед" data-language-autonym="Български" data-language-local-name="búlgaro" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Ortoedre" title="Ortoedre – catalán" lang="ca" hreflang="ca" data-title="Ortoedre" data-language-autonym="Català" data-language-local-name="catalán" 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/%DA%95%D9%88%D9%88%DA%BE%D8%A7%D9%88%D8%A8%DB%95%D8%B1%DB%95%DB%8C_%DA%95%D8%A7%D8%B3%D8%AA_%DA%AF%DB%86%D8%B4%DB%95" title="ڕووھاوبەرەی ڕاست گۆشە – kurdo sorani" lang="ckb" hreflang="ckb" data-title="ڕووھاوبەرەی ڕاست گۆشە" data-language-autonym="کوردی" data-language-local-name="kurdo sorani" 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/Kv%C3%A1dr" title="Kvádr – checo" lang="cs" hreflang="cs" data-title="Kvádr" data-language-autonym="Čeština" data-language-local-name="checo" 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%A2%D3%B3%D1%80%C4%95_%D0%BA%C4%95%D1%82%D0%B5%D1%81%D0%BB%C4%95_%D0%BF%D0%B0%D1%80%D0%B0%D0%BB%D0%BB%D0%B5%D0%BB%D0%B5%D0%BF%D0%B8%D0%BF%D0%B5%D0%B4" title="Тӳрĕ кĕтеслĕ параллелепипед – chuvasio" lang="cv" hreflang="cv" data-title="Тӳрĕ кĕтеслĕ параллелепипед" data-language-autonym="Чӑвашла" data-language-local-name="chuvasio" 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/Ciwboid" title="Ciwboid – galés" lang="cy" hreflang="cy" data-title="Ciwboid" data-language-autonym="Cymraeg" data-language-local-name="galés" 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/Kasse" title="Kasse – danés" lang="da" hreflang="da" data-title="Kasse" data-language-autonym="Dansk" data-language-local-name="danés" 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/Quader" title="Quader – alemán" lang="de" hreflang="de" data-title="Quader" 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/Rectangular_cuboid" title="Rectangular cuboid – inglés" lang="en" hreflang="en" data-title="Rectangular cuboid" 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/Briko_(geometrio)" title="Briko (geometrio) – esperanto" lang="eo" hreflang="eo" data-title="Briko (geometrio)" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Risttahukas" title="Risttahukas – estonio" lang="et" hreflang="et" data-title="Risttahukas" data-language-autonym="Eesti" data-language-local-name="estonio" 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/Ortoedro" title="Ortoedro – euskera" lang="eu" hreflang="eu" data-title="Ortoedro" data-language-autonym="Euskara" data-language-local-name="euskera" 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_%D9%85%D8%B3%D8%AA%D8%B7%DB%8C%D9%84" title="مکعب مستطیل – persa" lang="fa" hreflang="fa" data-title="مکعب مستطیل" data-language-autonym="فارسی" data-language-local-name="persa" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Suorakulmainen_s%C3%A4rmi%C3%B6" title="Suorakulmainen särmiö – finés" lang="fi" hreflang="fi" data-title="Suorakulmainen särmiö" data-language-autonym="Suomi" data-language-local-name="finés" 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/Pav%C3%A9_droit" title="Pavé droit – francés" lang="fr" hreflang="fr" data-title="Pavé droit" data-language-autonym="Français" data-language-local-name="francés" 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/Sjauerkaant" title="Sjauerkaant – frisón septentrional" lang="frr" hreflang="frr" data-title="Sjauerkaant" data-language-autonym="Nordfriisk" data-language-local-name="frisón septentrional" 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%C3%B3ideach" title="Ciúbóideach – irlandés" lang="ga" hreflang="ga" data-title="Ciúbóideach" data-language-autonym="Gaeilge" data-language-local-name="irlandés" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%AA%D7%99%D7%91%D7%94_(%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94)" title="תיבה (גאומטריה) – hebreo" lang="he" hreflang="he" data-title="תיבה (גאומטריה)" data-language-autonym="עברית" data-language-local-name="hebreo" 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%BE%E0%A4%AD" title="घनाभ – hindi" lang="hi" hreflang="hi" data-title="घनाभ" 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/Kvadar" title="Kvadar – croata" lang="hr" hreflang="hr" data-title="Kvadar" data-language-autonym="Hrvatski" data-language-local-name="croata" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/T%C3%A9glatest" title="Téglatest – húngaro" lang="hu" hreflang="hu" data-title="Téglatest" data-language-autonym="Magyar" data-language-local-name="húngaro" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Balok" title="Balok – indonesio" lang="id" hreflang="id" data-title="Balok" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesio" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Cuboide_(geometria)" title="Cuboide (geometria) – italiano" lang="it" hreflang="it" data-title="Cuboide (geometria)" data-language-autonym="Italiano" data-language-local-name="italiano" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%9B%B4%E6%96%B9%E4%BD%93" title="直方体 – japonés" lang="ja" hreflang="ja" data-title="直方体" 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-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A7%81%EC%9C%A1%EB%A9%B4%EC%B2%B4" title="직육면체 – coreano" lang="ko" hreflang="ko" data-title="직육면체" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%8A%E0%BA%BB%E0%BA%87%E0%BA%AA%E0%BA%B5%E0%BB%88%E0%BB%81%E0%BA%88%E0%BA%A1%E0%BA%B8%E0%BA%99%E0%BA%AA%E0%BA%B2%E0%BA%81" title="ຊົງສີ່ແຈມຸນສາກ – lao" lang="lo" hreflang="lo" data-title="ຊົງສີ່ແຈມຸນສາກ" 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/Sta%C4%8Diakampis_gretasienis" title="Stačiakampis gretasienis – lituano" lang="lt" hreflang="lt" data-title="Stačiakampis gretasienis" 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/Taisnst%C5%ABra_paral%C4%93lskaldnis" title="Taisnstūra paralēlskaldnis – letón" lang="lv" hreflang="lv" data-title="Taisnstūra paralēlskaldnis" data-language-autonym="Latviešu" data-language-local-name="letón" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%B4%D0%B0%D1%80" title="Квадар – macedonio" lang="mk" hreflang="mk" data-title="Квадар" data-language-autonym="Македонски" data-language-local-name="macedonio" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Balk_(meetkunde)" title="Balk (meetkunde) – neerlandés" lang="nl" hreflang="nl" data-title="Balk (meetkunde)" data-language-autonym="Nederlands" data-language-local-name="neerlandés" class="interlanguage-link-target"><span>Nederlands</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%BE%E0%A8%B5" title="ਘਣਾਵ – punyabí" lang="pa" hreflang="pa" data-title="ਘਣਾਵ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="punyabí" 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/Prostopad%C5%82o%C5%9Bcian" title="Prostopadłościan – polaco" lang="pl" hreflang="pl" data-title="Prostopadłościan" data-language-autonym="Polski" data-language-local-name="polaco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Ortoedro" title="Ortoedro – portugués" lang="pt" hreflang="pt" data-title="Ortoedro" data-language-autonym="Português" data-language-local-name="portugués" 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/Suqtawask%27a" title="Suqtawask'a – quechua" lang="qu" hreflang="qu" data-title="Suqtawask'a" 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/Paralelipiped_dreptunghic" title="Paralelipiped dreptunghic – rumano" lang="ro" hreflang="ro" data-title="Paralelipiped dreptunghic" 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%9F%D1%80%D1%8F%D0%BC%D0%BE%D1%83%D0%B3%D0%BE%D0%BB%D1%8C%D0%BD%D1%8B%D0%B9_%D0%BF%D0%B0%D1%80%D0%B0%D0%BB%D0%BB%D0%B5%D0%BB%D0%B5%D0%BF%D0%B8%D0%BF%D0%B5%D0%B4" title="Прямоугольный параллелепипед – ruso" lang="ru" hreflang="ru" data-title="Прямоугольный параллелепипед" data-language-autonym="Русский" data-language-local-name="ruso" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Kvadar" title="Kvadar – serbocroata" lang="sh" hreflang="sh" data-title="Kvadar" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbocroata" 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/Rectangular_cuboid" title="Rectangular cuboid – cingalés" lang="si" hreflang="si" data-title="Rectangular cuboid" data-language-autonym="සිංහල" data-language-local-name="cingalés" 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/Cuboid" title="Cuboid – Simple English" lang="en-simple" hreflang="en-simple" data-title="Cuboid" 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/Kv%C3%A1der" title="Kváder – eslovaco" lang="sk" hreflang="sk" data-title="Kváder" data-language-autonym="Slovenčina" data-language-local-name="eslovaco" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Kvader" title="Kvader – esloveno" lang="sl" hreflang="sl" data-title="Kvader" data-language-autonym="Slovenščina" data-language-local-name="esloveno" 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/Salxaale" title="Salxaale – somalí" lang="so" hreflang="so" data-title="Salxaale" data-language-autonym="Soomaaliga" data-language-local-name="somalí" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%B4%D0%B0%D1%80" title="Квадар – serbio" lang="sr" hreflang="sr" data-title="Квадар" data-language-autonym="Српски / srpski" data-language-local-name="serbio" 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/Balok" title="Balok – sundanés" lang="su" hreflang="su" data-title="Balok" data-language-autonym="Sunda" data-language-local-name="sundanés" 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/R%C3%A4tblock" title="Rätblock – sueco" lang="sv" hreflang="sv" data-title="Rätblock" data-language-autonym="Svenska" data-language-local-name="sueco" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AE%A9%E0%AE%9A%E0%AF%86%E0%AE%B5%E0%AF%8D%E0%AE%B5%E0%AE%95%E0%AE%AE%E0%AF%8D" title="கனசெவ்வகம் – tamil" lang="ta" hreflang="ta" data-title="கனசெவ்வகம்" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%97%E0%B8%A3%E0%B8%87%E0%B8%AA%E0%B8%B5%E0%B9%88%E0%B9%80%E0%B8%AB%E0%B8%A5%E0%B8%B5%E0%B9%88%E0%B8%A2%E0%B8%A1%E0%B8%A1%E0%B8%B8%E0%B8%A1%E0%B8%89%E0%B8%B2%E0%B8%81" title="ทรงสี่เหลี่ยมมุมฉาก – tailandés" lang="th" hreflang="th" data-title="ทรงสี่เหลี่ยมมุมฉาก" data-language-autonym="ไทย" data-language-local-name="tailandés" 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/Dikd%C3%B6rtgenler_prizmas%C4%B1" title="Dikdörtgenler prizması – turco" lang="tr" hreflang="tr" data-title="Dikdörtgenler prizması" 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%9F%D1%80%D1%8F%D0%BC%D0%BE%D0%BA%D1%83%D1%82%D0%BD%D0%B8%D0%B9_%D0%BF%D0%B0%D1%80%D0%B0%D0%BB%D0%B5%D0%BB%D0%B5%D0%BF%D1%96%D0%BF%D0%B5%D0%B4" title="Прямокутний паралелепіпед – ucraniano" lang="uk" hreflang="uk" data-title="Прямокутний паралелепіпед" data-language-autonym="Українська" data-language-local-name="ucraniano" 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_%D9%86%D9%85%D8%A7" title="مکعب نما – urdu" lang="ur" hreflang="ur" data-title="مکعب نما" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%C3%ACnh_h%E1%BB%99p_ch%E1%BB%AF_nh%E1%BA%ADt" title="Hình hộp chữ nhật – vietnamita" lang="vi" hreflang="vi" 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class="mw-redirect" title="Cuboide rectangular">Cuboide rectangular</a>»)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="es" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r157776694">.mw-parser-output .infobox .imagen{max-width:100%;margin:0 auto}.mw-parser-output .infobox .imagen img{max-width:100%;height:auto}.mw-parser-output .infobox .mw-kartographer-container .thumbinner,.mw-parser-output .infobox .mw-kartographer-map{box-sizing:border-box;width:100%!important}body.skin-timeless .mw-parser-output .infobox .imagen a.image>img{max-width:100%!important;height:auto!important}</style><table class="infobox" style="width:22.7em; line-height: 1.4em; text-align:left; padding:.23em;width:280px;;"><tbody><tr><th colspan="3" class="cabecera ingeniería" style="text-align:center;background-color:transparent;color:inherit;background-color:#F8B000; color:#000000};;">Ortoedro</th></tr><tr><td colspan="3" style="text-align:center;background-color:#FCC84B; font-size:105%; padding:3px; font-style:italic; text-align:right;;"> Familia: <a href="/wiki/Prisma_(geometr%C3%ADa)" title="Prisma (geometría)">Prisma</a> <a href="/wiki/Grupo_diedral" class="mw-redirect" title="Grupo diedral">Grupo diedral</a></td></tr><tr><td colspan="3" class="imagen" style="text-align:center;width:65%; vertical-align:middle; padding:3px;"> <span typeof="mw:File"><a href="/wiki/Archivo:Parallelepipede.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Parallelepipede.png/200px-Parallelepipede.png" decoding="async" width="200" height="142" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Parallelepipede.png/300px-Parallelepipede.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Parallelepipede.png/400px-Parallelepipede.png 2x" data-file-width="500" data-file-height="355" /></a></span><br /><div style="display:inline;font-size:90%;">Imagen del sólido</div></td></tr><tr><th scope="row" style="text-align:left;background-color:#FDD676; width:35%; vertical-align:middle; padding:3px;"><a href="/wiki/Cara_(geometr%C3%ADa)" title="Cara (geometría)">Caras</a></th><td colspan="2" style="width:65%; vertical-align:middle; padding:3px;"> 6</td></tr><tr><th scope="row" style="text-align:left;background-color:#FDD676; width:35%; vertical-align:middle; padding:3px;"><a href="/wiki/Arista_(geometr%C3%ADa)" title="Arista (geometría)">Aristas</a></th><td colspan="2" style="width:65%; vertical-align:middle; padding:3px;"> 12</td></tr><tr><th scope="row" style="text-align:left;background-color:#FDD676; width:35%; vertical-align:middle; padding:3px;"><a href="/wiki/V%C3%A9rtice_(geometr%C3%ADa)" title="Vértice (geometría)">Vértices</a></th><td colspan="2" style="width:65%; vertical-align:middle; padding:3px;"> 8</td></tr><tr><th scope="row" style="text-align:left;background-color:#FDD676; width:35%; vertical-align:middle; padding:3px;"><a href="/wiki/Configuraci%C3%B3n_de_v%C3%A9rtices" title="Configuración de vértices">Configuración de vértices</a></th><td colspan="2" style="width:65%; vertical-align:middle; padding:3px;"> 4 en cada cara. 3 caras concurrentes en cada uno.</td></tr><tr><th scope="row" style="text-align:left;background-color:#FDD676; width:35%; vertical-align:middle; padding:3px;"><a href="/wiki/Grupo_de_simetr%C3%ADa" title="Grupo de simetría">Grupo de simetría</a></th><td colspan="2" style="width:65%; vertical-align:middle; padding:3px;"> (<i>D</i><sub>2<i>h</i></sub>)</td></tr><tr><th colspan="3" style="text-align:center;background-color:#FBC237; padding:3px;">Propiedades</th></tr><tr><td colspan="3" style="text-align:center;width:65%; vertical-align:middle; padding:3px;"> <a href="/wiki/Convexidad" title="Convexidad">Convexo</a></td></tr><tr><td class="noprint" colspan="3" style="text-align:left;"><div class="plainlinks wikidata-link" style="font-size: 0.85em">[<a href="https://www.wikidata.org/wiki/Q262959" class="extiw" title="d:Q262959">editar datos en Wikidata</a>]</div></td></tr></tbody></table> <p>Un <b>ortoedro</b> es un <a href="/wiki/Prisma_(geometr%C3%ADa)" title="Prisma (geometría)">prisma</a> <a href="/wiki/Rectangular" class="mw-redirect" title="Rectangular">rectangular</a> <a href="/wiki/Ortogonal" class="mw-redirect" title="Ortogonal">ortogonal</a>, cuyas <a href="/wiki/Cara_(geometr%C3%ADa)" title="Cara (geometría)">caras</a> forman entre sí <a href="/wiki/%C3%81ngulo_diedro" title="Ángulo diedro">ángulos diedros</a> <a href="/wiki/%C3%81ngulo_recto" title="Ángulo recto">rectos</a>. A estos <b><a href="/wiki/Prisma_(geometr%C3%ADa)" title="Prisma (geometría)">prismas</a> rectos</b> se los denomina <b><a href="/wiki/Paralelep%C3%ADpedo" title="Paralelepípedo">paralelepípedos</a> <a href="/wiki/Rectangular" class="mw-redirect" title="Rectangular">rectangulares</a></b>. Habitualmente se las identifica con cajas como las de zapatos, ladrillos o, si está de pie, con la forma de una <a href="/wiki/Torre" title="Torre">torre</a>.<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>​ Las caras opuestas de un ortoedro son iguales entre sí. </p><p>El <a href="/wiki/Cubo" title="Cubo">cubo</a> es un caso especial de ortoedro, de seis <a href="/wiki/Cara_(geometr%C3%ADa)" title="Cara (geometría)">caras</a> <a href="/wiki/Cuadrado" title="Cuadrado">cuadradas</a> iguales. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Fórmulas_del_ortoedro"><span id="F.C3.B3rmulas_del_ortoedro"></span>Fórmulas del ortoedro</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ortoedro&action=edit&section=1" title="Editar sección: Fórmulas del ortoedro"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Si llamamos <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\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d73aa5354c24942dab5316be466465a9d171510" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.617ex; height:1.676ex;" alt="{\displaystyle a\,}" /></span> al <a href="/wiki/Ancho" title="Ancho">ancho</a> o profundidad de un ortoedro, <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\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b1bcf19f4ec75b1d2cc0be001e58a314fb0a940" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.385ex; height:2.176ex;" alt="{\displaystyle b\,}" /></span> a su <a href="/wiki/Alto_dimensional" class="mw-redirect" title="Alto dimensional">altura</a> y <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 c\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8573e7d95140b0d4068258d8162e189563baee6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.394ex; height:1.676ex;" alt="{\displaystyle c\,}" /></span> a su <a href="/wiki/Longitud_dimensional" class="mw-redirect" title="Longitud dimensional">longitud</a>, podemos definir las siguientes fórmulas: </p> <div class="mw-heading mw-heading3"><h3 id="Áreas"><span id=".C3.81reas"></span>Áreas</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ortoedro&action=edit&section=2" title="Editar sección: Áreas"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>El <a href="/wiki/%C3%81rea" title="Área">área</a> total del paralelepípedo es igual a la suma de las respectivas áreas de sus 6 caras, que al estar repetidas 2 veces, se pueden calcular como: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\,=\,2\cdot a\cdot b+2\cdot a\cdot c+2\cdot b\cdot c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mspace width="thinmathspace"></mspace> <mo>=</mo> <mspace width="thinmathspace"></mspace> <mn>2</mn> <mo>⋅<!-- ⋅ --></mo> <mi>a</mi> <mo>⋅<!-- ⋅ --></mo> <mi>b</mi> <mo>+</mo> <mn>2</mn> <mo>⋅<!-- ⋅ --></mo> <mi>a</mi> <mo>⋅<!-- ⋅ --></mo> <mi>c</mi> <mo>+</mo> <mn>2</mn> <mo>⋅<!-- ⋅ --></mo> <mi>b</mi> <mo>⋅<!-- ⋅ --></mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\,=\,2\cdot a\cdot b+2\cdot a\cdot c+2\cdot b\cdot c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/beaab0f5704b57be453ff71cfa219e1abb6daa66" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:31.327ex; height:2.343ex;" alt="{\displaystyle A\,=\,2\cdot a\cdot b+2\cdot a\cdot c+2\cdot b\cdot c}" /></span></dd></dl> <p>O lo que es lo mismo: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\,=\,2\cdot (a\cdot b+a\cdot c+b\cdot c)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mspace width="thinmathspace"></mspace> <mo>=</mo> <mspace width="thinmathspace"></mspace> <mn>2</mn> <mo>⋅<!-- ⋅ --></mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>⋅<!-- ⋅ --></mo> <mi>b</mi> <mo>+</mo> <mi>a</mi> <mo>⋅<!-- ⋅ --></mo> <mi>c</mi> <mo>+</mo> <mi>b</mi> <mo>⋅<!-- ⋅ --></mo> <mi>c</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\,=\,2\cdot (a\cdot b+a\cdot c+b\cdot c)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e05292d90c818f8ea4d87e51ae1ba0f138d8239" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.453ex; height:2.843ex;" alt="{\displaystyle A\,=\,2\cdot (a\cdot b+a\cdot c+b\cdot c)}" /></span></dd></dl> <p>Por su parte, el cálculo del <b>área lateral</b> será análogo, pero omitiendo las bases superior e inferior: </p><p><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_{l}\,=\,2\cdot a\cdot b+2\cdot b\cdot c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mspace width="thinmathspace"></mspace> <mo>=</mo> <mspace width="thinmathspace"></mspace> <mn>2</mn> <mo>⋅<!-- ⋅ --></mo> <mi>a</mi> <mo>⋅<!-- ⋅ --></mo> <mi>b</mi> <mo>+</mo> <mn>2</mn> <mo>⋅<!-- ⋅ --></mo> <mi>b</mi> <mo>⋅<!-- ⋅ --></mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{l}\,=\,2\cdot a\cdot b+2\cdot b\cdot c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/527f9cf70bcf57392838e579ff7408aa711b7a05" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:22.452ex; height:2.509ex;" alt="{\displaystyle A_{l}\,=\,2\cdot a\cdot b+2\cdot b\cdot c}" /></span> </p><p>También se puede calcular como el producto del <a href="/wiki/Per%C3%ADmetro" title="Perímetro">perímetro</a> de la base por la altura. </p> <figure class="mw-halign-right" typeof="mw:File"><a href="/wiki/Archivo:Pitagoras_en_el_espacio.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Pitagoras_en_el_espacio.png/250px-Pitagoras_en_el_espacio.png" decoding="async" width="250" height="161" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Pitagoras_en_el_espacio.png/375px-Pitagoras_en_el_espacio.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/94/Pitagoras_en_el_espacio.png/500px-Pitagoras_en_el_espacio.png 2x" data-file-width="652" data-file-height="419" /></a><figcaption></figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Volumen">Volumen</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ortoedro&action=edit&section=3" title="Editar sección: Volumen"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-left" typeof="mw:File"><a href="/wiki/Archivo:Ortoedro.png" class="mw-file-description" title="Un ortoedro visto en perspectiva caballera y acotado"><img alt="Un ortoedro visto en perspectiva caballera y acotado" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Ortoedro.png/200px-Ortoedro.png" decoding="async" width="200" height="116" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Ortoedro.png/300px-Ortoedro.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/Ortoedro.png/400px-Ortoedro.png 2x" data-file-width="1024" data-file-height="594" /></a><figcaption>Un ortoedro visto en perspectiva caballera y acotado</figcaption></figure> <p>El <a href="/wiki/Volumen_(geometr%C3%ADa)" class="mw-redirect" title="Volumen (geometría)">volumen</a> del ortoedro se calcula, al igual que el de cualquier prisma recto, multiplicando el área de la <a href="/wiki/Base_(geometr%C3%ADa)" title="Base (geometría)">base</a> B<sub>or</sub> por la altura h<sub>or</sub>. Dado que la base es un <a href="/wiki/Rect%C3%A1ngulo" title="Rectángulo">rectángulo</a>, y el área del rectángulo es igual al producto de su base b<sub>R</sub> por altura h<sub>R</sub> o el producto de sus lados contiguos, se puede calcular el volumen del ortoedro como </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V\,=\,a\cdot b\cdot c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mspace width="thinmathspace"></mspace> <mo>=</mo> <mspace width="thinmathspace"></mspace> <mi>a</mi> <mo>⋅<!-- ⋅ --></mo> <mi>b</mi> <mo>⋅<!-- ⋅ --></mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V\,=\,a\cdot b\cdot c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45620eeff64d22cfbfd72af75b7cb2b87e3b4850" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.252ex; height:2.176ex;" alt="{\displaystyle V\,=\,a\cdot b\cdot c}" /></span> </p> <div class="mw-heading mw-heading3"><h3 id="Diagonal">Diagonal</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ortoedro&action=edit&section=4" title="Editar sección: Diagonal"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Considérese una cara (rectángulo) trace su diagonal de tal polígono. Por uno de sus extremos trace una arísta perpendicular. Se une el primer extremo de la diagonal del rectángulo con el extremo de la arista, fuera del plano de la cara; tal segmento es una <b>diagonal</b> del ortoedro. Basándonos en el <a href="/wiki/Teorema_de_Pit%C3%A1goras" title="Teorema de Pitágoras">Teorema de Pitágoras</a> podemos calcular la diagonal espacial del ortoedro de la siguiente forma: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D\,=\,{\sqrt {a^{2}+b^{2}+c^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mspace width="thinmathspace"></mspace> <mo>=</mo> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D\,=\,{\sqrt {a^{2}+b^{2}+c^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4616b076603b74896139f733860f61d6c29aa66a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.198ex; height:3.509ex;" alt="{\displaystyle D\,=\,{\sqrt {a^{2}+b^{2}+c^{2}}}}" /></span> </p> <div class="mw-heading mw-heading2"><h2 id="Notas_y_referencias">Notas y referencias</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ortoedro&action=edit&section=5" title="Editar sección: Notas y 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 class="citation web"><a rel="nofollow" class="external text" href="https://www.gaussianos.com/la-caja-de-euler/">«La caja de Euler»</a>. <i>Gaussianos</i>. 7 de mayo de 2007<span class="reference-accessdate">. Consultado el 17 de abril de 2020</span>.</span><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fes.wikipedia.org%3AOrtoedro&rft.atitle=La+caja+de+Euler&rft.date=7+de+mayo+de+2007&rft.genre=article&rft.jtitle=Gaussianos&rft_id=https%3A%2F%2Fwww.gaussianos.com%2Fla-caja-de-euler%2F&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div> <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=Ortoedro&action=edit&section=6" title="Editar sección: Véase también"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Ortoedro_%C3%A1ureo" title="Ortoedro áureo">Ortoedro áureo</a></li> <li><a href="/wiki/Hiperrect%C3%A1ngulo" title="Hiperrectángulo">Ortotopo</a></li> <li><a href="/wiki/Paralelep%C3%ADpedo" title="Paralelepípedo">Paralelepípedo</a></li> <li><a href="/wiki/Teorema_de_Pit%C3%A1goras" title="Teorema de Pitágoras">Teorema de Pitágoras</a></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=Ortoedro&action=edit&section=7" title="Editar sección: Enlaces externos"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png" decoding="async" width="15" height="20" 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" /></span></span> <a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons">Wikimedia Commons</a> alberga una categoría multimedia sobre <b><a href="https://commons.wikimedia.org/wiki/Category:Cuboids" class="extiw" title="commons:Category:Cuboids">Ortoedro</a></b>.</li> <li><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/20px-Wiktionary-logo.svg.png" decoding="async" width="20" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/30px-Wiktionary-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/40px-Wiktionary-logo.svg.png 2x" data-file-width="370" data-file-height="350" /></span></span> <a href="/wiki/Wikcionario" title="Wikcionario">Wikcionario</a> tiene definiciones y otra información sobre <b><a href="https://es.wiktionary.org/wiki/ortoedro" class="extiw" title="wikt:ortoedro">ortoedro</a></b>.</li> <li><a rel="nofollow" class="external text" href="http://recursostic.educacion.es/descartes/web/materiales_didacticos/Volumenes_d3/index.htm">Volumen</a>, <a rel="nofollow" class="external text" href="http://recursostic.educacion.es/descartes/web/materiales_didacticos/Areas_2eso_d3/index.htm">área</a> y <a rel="nofollow" class="external text" href="http://recursostic.educacion.es/descartes/web/materiales_didacticos/desarrollo_ortoedro/Desarrollo_Ortoedro.htm">desarrollo del ortoedro</a></li> <li><span id="Reference-Mathworld-Ortoedro" 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/Cuboid.html">«Ortoedro»</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%3AOrtoedro&rft.atitle=Ortoedro&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%2FCuboid.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></li> <li><a rel="nofollow" class="external text" href="http://www.korthalsaltes.com/es/model.php?name_en=rectangular%20prism">Ortoedros de papel</a></li> <li><a rel="nofollow" class="external text" href="http://www.solin.16mb.com/geometria/diagonal_paralelepipedo/index.htm">Diagonal del paralelepípedo oblicuo.</a></li></ul> <style data-mw-deduplicate="TemplateStyles:r161257576">.mw-parser-output .mw-authority-control{margin-top:1.5em}.mw-parser-output .mw-authority-control .navbox table{margin:0}.mw-parser-output .mw-authority-control .navbox hr:last-child{display:none}.mw-parser-output .mw-authority-control .navbox+.mw-mf-linked-projects{display:none}.mw-parser-output .mw-authority-control .mw-mf-linked-projects{display:flex;padding:0.5em;border:1px solid var(--border-color-base,#a2a9b1);background-color:var(--background-color-neutral,#eaecf0);color:var(--color-base,#202122)}.mw-parser-output .mw-authority-control .mw-mf-linked-projects ul li{margin-bottom:0}.mw-parser-output .mw-authority-control .navbox{border:1px solid var(--border-color-base,#a2a9b1);background-color:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .mw-authority-control .navbox-list{border-color:#f8f9fa}.mw-parser-output .mw-authority-control .navbox th{background-color:#eeeeff}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .mw-mf-linked-projects{border:1px solid var(--border-color-base,#72777d);background-color:var(--background-color-neutral,#27292d);color:var(--color-base,#eaecf0)}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .navbox{border:1px solid var(--border-color-base,#72777d)!important;background-color:var(--background-color-neutral-subtle,#202122)!important}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .navbox-list{border-color:#202122!important}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .navbox th{background-color:#27292d!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .mw-mf-linked-projects{border:1px solid var(--border-color-base,#72777d)!important;background-color:var(--background-color-neutral,#27292d)!important;color:var(--color-base,#eaecf0)!important}html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .navbox{border:1px solid var(--border-color-base,#72777d)!important;background-color:var(--background-color-neutral-subtle,#202122)!important}html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .navbox-list{border-color:#202122!important}html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .navbox th{background-color:#27292d!important}}</style><div class="mw-authority-control"><div role="navigation" class="navbox" aria-label="Navbox" style="width: inherit;padding:3px"><table class="hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width: 12%; text-align:center;"><a href="/wiki/Control_de_autoridades" title="Control de autoridades">Control de autoridades</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><b>Proyectos Wikimedia</b></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikidata" title="Wikidata"><img alt="Wd" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></a></span> Datos:</span> <span class="uid"><a href="https://www.wikidata.org/wiki/Q262959" class="extiw" title="wikidata:Q262959">Q262959</a></span></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikimedia_Commons" title="Commonscat"><img alt="Commonscat" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png" decoding="async" width="15" height="20" 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> Multimedia:</span> <span class="uid"><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Rectangular_cuboids">Rectangular cuboids</a></span> / <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Special:MediaSearch?type=image&search=%22Q262959%22">Q262959</a></span></span></li></ul> <hr /> <ul><li><b>Identificadores</b></li> <li><span style="white-space:nowrap;"><a href="/wiki/Gemeinsame_Normdatei" title="Gemeinsame Normdatei">GND</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4322444-1">4322444-1</a></span></li></ul> </div></td></tr></tbody></table></div><div class="mw-mf-linked-projects hlist"> <ul><li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikidata" title="Wikidata"><img alt="Wd" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></a></span> Datos:</span> <span class="uid"><a href="https://www.wikidata.org/wiki/Q262959" class="extiw" title="wikidata:Q262959">Q262959</a></span></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikimedia_Commons" title="Commonscat"><img alt="Commonscat" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png" decoding="async" width="15" height="20" 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> Multimedia:</span> <span class="uid"><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Rectangular_cuboids">Rectangular cuboids</a></span> / <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Special:MediaSearch?type=image&search=%22Q262959%22">Q262959</a></span></span></li></ul> </div></div> <!-- NewPP limit report Parsed by mw‐web.eqiad.main‐b8b46b654‐6dvw2 Cached time: 20250317191545 Cache expiry: 2592000 Reduced expiry: false Complications: [show‐toc] CPU time usage: 0.193 seconds Real time usage: 0.587 seconds Preprocessor visited node count: 1297/1000000 Post‐expand include size: 15554/2097152 bytes Template argument size: 350/2097152 bytes Highest expansion depth: 8/100 Expensive parser function count: 2/500 Unstrip recursion depth: 0/20 Unstrip post‐expand size: 4270/5000000 bytes Lua time usage: 0.114/10.000 seconds Lua memory usage: 3527345/52428800 bytes Number of Wikibase entities loaded: 3/400 --> <!-- Transclusion expansion time report (%,ms,calls,template) 100.00% 249.193 1 -total 41.09% 102.393 1 Plantilla:Control_de_autoridades 32.52% 81.040 1 Plantilla:Ficha_de_poliedro 31.51% 78.529 1 Plantilla:Ficha 13.47% 33.562 1 Plantilla:Listaref 13.08% 32.594 2 Plantilla:Cita_web 9.84% 24.522 1 Plantilla:Commonscat 5.94% 14.814 1 Plantilla:Propiedad 2.76% 6.881 5 Plantilla:RGB 1.73% 4.317 1 Plantilla:Título_sin_coletilla --> <!-- Saved in parser cache with key eswiki:pcache:675186:|#|:idhash:canonical and timestamp 20250317191545 and revision id 161999895. 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