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mw-ui-icon-wikimedia-logIn"></span> <span>登录</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> 未登录编辑者的页面 <a href="/wiki/Help:%E6%96%B0%E6%89%8B%E5%85%A5%E9%97%A8" aria-label="了解有关编辑的更多信息"><span>了解详情</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/Special:%E6%88%91%E7%9A%84%E8%B4%A1%E7%8C%AE" title="来自此IP地址的编辑列表[y]" accesskey="y"><span>贡献</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%AE%A8%E8%AE%BA%E9%A1%B5" title="对于来自此IP地址编辑的讨论[n]" accesskey="n"><span>讨论</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 class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="站点"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="目录" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">目录</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">隐藏</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">序言</div> </a> </li> <li id="toc-維面" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#維面"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>維面</span> </div> </a> <button aria-controls="toc-維面-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>开关維面子章节</span> </button> <ul id="toc-維面-sublist" class="vector-toc-list"> <li id="toc-多面體的維面" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#多面體的維面"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>多面體的維面</span> </div> </a> <ul id="toc-多面體的維面-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-多胞形的維面" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#多胞形的維面"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>多胞形的維面</span> </div> </a> <ul id="toc-多胞形的維面-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-单纯复形的維面" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#单纯复形的維面"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>单纯复形的維面</span> </div> </a> <ul id="toc-单纯复形的維面-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-多維面" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#多維面"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>多維面</span> </div> </a> <button aria-controls="toc-多維面-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>开关多維面子章节</span> </button> <ul id="toc-多維面-sublist" class="vector-toc-list"> <li id="toc-負一維面" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#負一維面"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>負一維面</span> </div> </a> <ul id="toc-負一維面-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-零維面" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#零維面"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>零維面</span> </div> </a> <ul id="toc-零維面-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-一維面" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#一維面"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>一維面</span> </div> </a> <ul id="toc-一維面-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-二維面" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#二維面"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>二維面</span> </div> </a> <ul id="toc-二維面-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-三維或更高維度的面" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#三維或更高維度的面"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>三維或更高維度的面</span> </div> </a> <ul id="toc-三維或更高維度的面-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-n維面" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#n維面"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>n維面</span> </div> </a> <ul id="toc-n維面-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-(n-1)維面" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#(n-1)維面"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.7</span> <span>(n-1)維面</span> </div> </a> <ul id="toc-(n-1)維面-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-(n-2)維面" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#(n-2)維面"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.8</span> <span>(n-2)維面</span> </div> </a> <ul id="toc-(n-2)維面-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-(n-3)維面" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#(n-3)維面"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.9</span> <span>(n-3)維面</span> </div> </a> <ul id="toc-(n-3)維面-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-參見" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#參見"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>參見</span> </div> </a> <ul id="toc-參見-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-參考文獻" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#參考文獻"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>參考文獻</span> </div> </a> <ul id="toc-參考文獻-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-外部連結" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#外部連結"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>外部連結</span> </div> </a> <ul id="toc-外部連結-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="目录" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="目录" > <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="开关目录" > <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">开关目录</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">維面</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="前往另一种语言写成的文章。8种语言可用" > <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-8" 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">8种语言</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Facet_(geometry)" title="Facet (geometry) – 英语" lang="en" hreflang="en" data-title="Facet (geometry)" data-language-autonym="English" data-language-local-name="英语" 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/Faceto_(geometrio)" title="Faceto (geometrio) – 世界语" lang="eo" hreflang="eo" data-title="Faceto (geometrio)" data-language-autonym="Esperanto" data-language-local-name="世界语" 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/Faceta_(geometr%C3%ADa)" title="Faceta (geometría) – 西班牙语" lang="es" hreflang="es" data-title="Faceta (geometría)" data-language-autonym="Español" data-language-local-name="西班牙语" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Facet_(geometria)" title="Facet (geometria) – 意大利语" lang="it" hreflang="it" data-title="Facet (geometria)" data-language-autonym="Italiano" data-language-local-name="意大利语" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Fa%C8%9Bet%C4%83_(geometrie)" title="Fațetă (geometrie) – 罗马尼亚语" lang="ro" hreflang="ro" data-title="Fațetă (geometrie)" data-language-autonym="Română" data-language-local-name="罗马尼亚语" 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%A4%D0%B0%D1%81%D0%B5%D1%82%D0%B0_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F)" title="Фасета (геометрия) – 俄语" lang="ru" hreflang="ru" data-title="Фасета (геометрия)" data-language-autonym="Русский" data-language-local-name="俄语" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Faceta_(matematika)" title="Faceta (matematika) – 斯洛文尼亚语" lang="sl" hreflang="sl" data-title="Faceta (matematika)" data-language-autonym="Slovenščina" data-language-local-name="斯洛文尼亚语" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A4%D0%B0%D1%81%D0%B5%D1%82%D0%B0_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D1%96%D1%8F)" title="Фасета (геометрія) – 乌克兰语" lang="uk" hreflang="uk" data-title="Фасета (геометрія)" data-language-autonym="Українська" data-language-local-name="乌克兰语" class="interlanguage-link-target"><span>Українська</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/Q3847020#sitelinks-wikipedia" title="编辑跨语言链接" class="wbc-editpage">编辑链接</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="命名空间"> <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/%E7%B6%AD%E9%9D%A2" title="浏览条目正文[c]" accesskey="c"><span>条目</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:%E7%B6%AD%E9%9D%A2" rel="discussion" title="关于此页面的讨论[t]" accesskey="t"><span>讨论</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown " > <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="更改语言变体" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button 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data-event-name="pinnable-header.vector-appearance.unpin">隐藏</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">维基百科，自由的百科全书</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">（重定向自<a href="/w/index.php?title=%E7%B6%AD%E5%B3%B0&redirect=no" class="mw-redirect" title="維峰">維峰</a>）</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="zh" dir="ltr"><p>在<a href="/wiki/%E5%B9%BE%E4%BD%95%E5%AD%B8" class="mw-redirect" title="幾何學">幾何學</a>中，<b>維面</b>（<b>Facet</b>）又稱為<b>超面</b>（<b>hyperface</b><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>）是指<a href="/wiki/%E5%87%A0%E4%BD%95%E5%BD%A2%E7%8A%B6" class="mw-redirect" title="几何形状">幾何形狀</a>的組成元素中，比該幾何形狀所在維度少一個維度的元素<sup id="cite_ref-MGZ_5-0" class="reference"><a href="#cite_note-MGZ-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>。也是任何<a href="/wiki/%E5%A4%9A%E8%83%9E%E5%BD%A2" title="多胞形">多胞形</a>的邊界。而若在維面前加一個整數則代表幾何形狀的組成元素中，維度為該數的元素，例如在立方體中2維面（2-Face）是指立方體的正方形面。一般來說，<b>維面</b>（<b>Facet</b>）不應與面（<b>Face</b>）混淆<sup id="cite_ref-Bridge_1974_6-0" class="reference"><a href="#cite_note-Bridge_1974-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Inchbald_2006_7-0" class="reference"><a href="#cite_note-Inchbald_2006-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>。一般的多胞形皆是以維面的數量命名，例如<a href="/wiki/%E5%85%AD%E9%82%8A%E5%BD%A2" class="mw-redirect" title="六邊形">六邊形</a>的維面是邊，其共有六條邊因此稱六邊形、<a href="/wiki/%E5%85%AB%E9%9D%A2%E9%AB%94" title="八面體">八面體</a>的維面是面，其共有八個面因此稱八面體。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="維面"><span id=".E7.B6.AD.E9.9D.A2"></span>維面</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B6%AD%E9%9D%A2&action=edit&section=1" title="编辑章节：維面"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>在<a href="/wiki/%E5%B9%BE%E4%BD%95%E5%AD%B8" class="mw-redirect" title="幾何學">幾何學</a>中，<b>維面</b>是<a href="/wiki/%E5%A4%9A%E9%9D%A2%E9%AB%94" class="mw-redirect" title="多面體">多面體</a>、<a href="/wiki/%E5%A4%9A%E8%83%9E%E5%BD%A2" title="多胞形">多胞形</a>或相關幾何結構的特徵之一，其通常可以用來描述該幾何結構的主要屬性。 </p> <div class="mw-heading mw-heading3"><h3 id="多面體的維面"><span id=".E5.A4.9A.E9.9D.A2.E9.AB.94.E7.9A.84.E7.B6.AD.E9.9D.A2"></span>多面體的維面</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B6%AD%E9%9D%A2&action=edit&section=2" title="编辑章节：多面體的維面"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>在三維幾何中，<a href="/wiki/%E5%A4%9A%E9%9D%A2%E9%AB%94" class="mw-redirect" title="多面體">多面體</a>的維面是指所有頂點都是多面體頂點的<a href="/wiki/%E5%A4%9A%E9%82%8A%E5%BD%A2" class="mw-redirect" title="多邊形">多邊形</a>面。在部分幾何結構中有可能存在不是維面的面<sup id="cite_ref-Bridge_1974_6-1" class="reference"><a href="#cite_note-Bridge_1974-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Inchbald_2006_7-1" class="reference"><a href="#cite_note-Inchbald_2006-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>。而維面重組，或稱刻面是指找到新的維面形成新的多面體的過程，這個過程有時可以稱作星形化，並可以套用到更高維度的幾何結構。 </p> <div class="mw-heading mw-heading3"><h3 id="多胞形的維面"><span id=".E5.A4.9A.E8.83.9E.E5.BD.A2.E7.9A.84.E7.B6.AD.E9.9D.A2"></span>多胞形的維面</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B6%AD%E9%9D%A2&action=edit&section=3" title="编辑章节：多胞形的維面"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>在<span class="ilh-all" data-orig-title="多面體組合學" data-lang-code="en" data-lang-name="英语" data-foreign-title="polyhedral combinatorics"><span class="ilh-page"><a href="/w/index.php?title=%E5%A4%9A%E9%9D%A2%E9%AB%94%E7%B5%84%E5%90%88%E5%AD%B8&action=edit&redlink=1" class="new" title="多面體組合學（页面不存在）">多面體組合學</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/polyhedral_combinatorics" class="extiw" title="en:polyhedral combinatorics"><span lang="en" dir="auto">polyhedral combinatorics</span></a></span><span class="ilh-paren">）</span></span></span>和一般的多胞形理論中，n維多胞形中的<i>n</i> − 1維元素稱為維面。維面也稱為(<i>n</i> − 1)維面、(<i>n</i> − 1)面或(<i>n</i> − 1)-面。而在在三維幾何學通常稱為面而不是<b>維面</b>。<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="单纯复形的維面"><span id=".E5.8D.95.E7.BA.AF.E5.A4.8D.E5.BD.A2.E7.9A.84.E7.B6.AD.E9.9D.A2"></span>单纯复形的維面</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B6%AD%E9%9D%A2&action=edit&section=4" title="编辑章节：单纯复形的維面"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>在<a href="/wiki/%E5%8D%95%E7%BA%AF%E5%A4%8D%E5%BD%A2" title="单纯复形">单纯复形</a>中，单纯复形的維面是一個单纯复形中最大的单纯形，且這個单纯形不是面也不是其他单纯复形的单纯形。<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup>對於单纯多胞形的邊界複合體，此定義與多面體組合學一致。 </p> <div class="mw-heading mw-heading2"><h2 id="多維面"><span id=".E5.A4.9A.E7.B6.AD.E9.9D.A2"></span>多維面</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B6%AD%E9%9D%A2&action=edit&section=5" title="编辑章节：多維面"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>在<a href="/wiki/%E5%B9%BE%E4%BD%95%E5%AD%B8" class="mw-redirect" title="幾何學">幾何學</a>中，維面一詞前面若加一個整數，則代表一幾何結構中維度為該整數的元素，此概念不應與維面混淆。例如k維面代表幾何結構中維度為k的元素，又稱<b>k面</b>、<b>k-面</b>或<b>k維元素</b>而在更高維度中，有時會稱為<b>k維胞</b>，這一用法並未限定元素的所屬維度。<sup id="cite_ref-m_2-1" class="reference"><a href="#cite_note-m-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-g_3-1" class="reference"><a href="#cite_note-g-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-z_4-1" class="reference"><a href="#cite_note-z-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>例如立方體的多維面包括了空多胞形（負一維面）、頂點（零維面）、邊（一維面）、正方形（二維面，一般稱面）和其本身（三維面，一般稱體）。正式地，對於一個多胞形<i>P</i>，多維面的定義是與一個「不與P內部相交的封閉半空間」的相交幾何結構（如交點、交線或交面等）<sup id="cite_ref-m_2-2" class="reference"><a href="#cite_note-m-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-z_4-2" class="reference"><a href="#cite_note-z-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>。多胞形中的多維面集合中同時也包含了多胞形本身和<a href="/wiki/%E7%A9%BA%E5%A4%9A%E8%83%9E%E5%BD%A2" title="空多胞形">空多胞形</a>。<sup id="cite_ref-g_3-2" class="reference"><a href="#cite_note-g-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-z_4-3" class="reference"><a href="#cite_note-z-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="負一維面"><span id=".E8.B2.A0.E4.B8.80.E7.B6.AD.E9.9D.A2"></span>負一維面</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B6%AD%E9%9D%A2&action=edit&section=6" title="编辑章节：負一維面"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:A_Square_and_its_Hasse_Diagram.PNG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/A_Square_and_its_Hasse_Diagram.PNG/360px-A_Square_and_its_Hasse_Diagram.PNG" decoding="async" width="360" height="186" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/4/49/A_Square_and_its_Hasse_Diagram.PNG 1.5x" data-file-width="517" data-file-height="267" /></a><figcaption>正方形中的負一維面、零維面、一維面和二維面。</figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r85100532">.mw-parser-output .hatnote{font-size:small}.mw-parser-output div.hatnote{padding-left:2em;margin-bottom:0.8em;margin-top:0.8em}.mw-parser-output .hatnote-notice-img::after{content:"\202f \202f \202f \202f "}.mw-parser-output .hatnote-notice-img-small::after{content:"\202f \202f "}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}body.skin-minerva .mw-parser-output .hatnote-notice-img,body.skin-minerva .mw-parser-output .hatnote-notice-img-small{display:none}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E7%A9%BA%E5%A4%9A%E8%83%9E%E5%BD%A2" title="空多胞形">空多胞形</a></div> <p><span class="anchor" id="空面"></span><span class="anchor" id="極小面"></span> 在抽象幾何學中，負一維面是<a href="/wiki/%E5%A4%9A%E8%83%9E%E5%BD%A2" title="多胞形">多胞形</a>中的元素集合中，不存在任何元素的子集，<sup id="cite_ref-Regular_Polytopes_book_10-0" class="reference"><a href="#cite_note-Regular_Polytopes_book-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>對應到<a href="/wiki/%E9%9B%86%E5%90%88%E8%AB%96" class="mw-redirect" title="集合論">集合論</a>中即為<a href="/wiki/%E7%A9%BA%E9%9B%86" title="空集">空集</a><sup id="cite_ref-article_johnson2003polytopes_11-0" class="reference"><a href="#cite_note-article_johnson2003polytopes-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>且所有<a href="/wiki/%E5%A4%9A%E8%83%9E%E5%BD%A2" title="多胞形">多胞形</a>都含有空多胞形<sup id="cite_ref-steelpillow_VertexFigures_12-0" class="reference"><a href="#cite_note-steelpillow_VertexFigures-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup>。這種面通常稱為多胞形的<b>極小面</b>（least face）<sup id="cite_ref-book_mcmullen2002abstract_13-0" class="reference"><a href="#cite_note-book_mcmullen2002abstract-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>、核維面或零化度（<span lang="en">nullity</span><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>）。 </p> <div class="mw-heading mw-heading3"><h3 id="零維面"><span id=".E9.9B.B6.E7.B6.AD.E9.9D.A2"></span>零維面</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B6%AD%E9%9D%A2&action=edit&section=7" title="编辑章节：零維面"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E9%A0%82%E9%BB%9E_(%E5%B9%BE%E4%BD%95)" title="頂點 (幾何)">頂點 (幾何)</a></div> <p>零維面為幾何結構中的零維元素，即頂點，通常由幾何結構的元素相交於點上形成。<sup id="cite_ref-Euclid_15-0" class="reference"><a href="#cite_note-Euclid-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="一維面"><span id=".E4.B8.80.E7.B6.AD.E9.9D.A2"></span>一維面</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B6%AD%E9%9D%A2&action=edit&section=8" title="编辑章节：一維面"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E9%82%8A_(%E5%B9%BE%E4%BD%95)" title="邊 (幾何)">邊 (幾何)</a></div> <p>一維面為幾何結構中的一維元素，即邊或稜，通常由二個或多個幾何結構的元素交於一線而形成。<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="二維面"><span id=".E4.BA.8C.E7.B6.AD.E9.9D.A2"></span>二維面</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B6%AD%E9%9D%A2&action=edit&section=9" title="编辑章节：二維面"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E9%9D%A2_(%E5%B9%BE%E4%BD%95)" title="面 (幾何)">面 (幾何)</a></div> <p>二維面為幾何結構中的二維元素，通常會省略前面的維度直接稱<b>面</b>。<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="三維或更高維度的面"><span id=".E4.B8.89.E7.B6.AD.E6.88.96.E6.9B.B4.E9.AB.98.E7.B6.AD.E5.BA.A6.E7.9A.84.E9.9D.A2"></span>三維或更高維度的面</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B6%AD%E9%9D%A2&action=edit&section=10" title="编辑章节：三維或更高維度的面"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E8%83%9E_(%E5%B9%BE%E4%BD%95)" class="mw-redirect" title="胞 (幾何)">胞 (幾何)</a></div> <p>三維或更高維度的面通常稱為胞<sup id="cite_ref-Regular_Polytopes_book_10-1" class="reference"><a href="#cite_note-Regular_Polytopes_book-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Mathworld_Cell_18-0" class="reference"><a href="#cite_note-Mathworld_Cell-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup>，更高維度的胞通常會以其維度稱呼，例如四維胞、五維胞等。<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-article_施开达1999正则多胞形和_20-0" class="reference"><a href="#cite_note-article_施开达1999正则多胞形和-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="n維面"><span id="n.E7.B6.AD.E9.9D.A2"></span>n維面</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B6%AD%E9%9D%A2&action=edit&section=11" title="编辑章节：n維面"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="anchor" id="體"></span><span class="anchor" id="極大面"></span><span class="anchor" id="非法面"></span> 若一個多胞形其維度就是n維，則n維面為該多胞形本身，通常稱為<b>體</b>，而在抽象幾何學中，也稱為<b>極大面</b>（Greatest Face）<sup id="cite_ref-book_mcmullen2002abstract_13-1" class="reference"><a href="#cite_note-book_mcmullen2002abstract-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>，並且與<a href="#極小面">極小面</a>合稱<b>非法面</b>（Improper Face）。<sup id="cite_ref-article_araujo2013colorful_21-0" class="reference"><a href="#cite_note-article_araujo2013colorful-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="(n-1)維面"><span id=".28n-1.29.E7.B6.AD.E9.9D.A2"></span>(n-1)維面</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B6%AD%E9%9D%A2&action=edit&section=12" title="编辑章节：(n-1)維面"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>若一個多胞形其維度就是n維，則其(n-1)維的元素稱為<b>維面</b>（Facet）<sup id="cite_ref-MGZ_5-1" class="reference"><a href="#cite_note-MGZ-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading3"><h3 id="(n-2)維面"><span id=".28n-2.29.E7.B6.AD.E9.9D.A2"></span>(n-2)維面</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B6%AD%E9%9D%A2&action=edit&section=13" title="编辑章节：(n-2)維面"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E7%BB%B4%E8%84%8A" title="维脊">維脊</a></div> <p>若一個多胞形其維度就是n維，則其(n-2)維的元素稱為<b>維脊</b>（Ridge）<sup id="cite_ref-MZ_22-0" class="reference"><a href="#cite_note-MZ-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading3"><h3 id="(n-3)維面"><span id=".28n-3.29.E7.B6.AD.E9.9D.A2"></span>(n-3)維面</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B6%AD%E9%9D%A2&action=edit&section=14" title="编辑章节：(n-3)維面"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E7%B6%AD%E5%B3%B0" class="mw-redirect" title="維峰">維峰</a></div> <p>若一個多胞形其維度就是n維，則其(n-3)維的元素稱為<b>維峰</b>（Peak）<sup id="cite_ref-article_nishio2017describing_23-0" class="reference"><a href="#cite_note-article_nishio2017describing-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading2"><h2 id="參見"><span id=".E5.8F.83.E8.A6.8B"></span>參見</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B6%AD%E9%9D%A2&action=edit&section=15" title="编辑章节：參見"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E9%9D%A2_(%E5%B9%BE%E4%BD%95)" title="面 (幾何)">面 (幾何)</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="參考文獻"><span id=".E5.8F.83.E8.80.83.E6.96.87.E7.8D.BB"></span>參考文獻</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B6%AD%E9%9D%A2&action=edit&section=16" title="编辑章节：參考文獻"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist columns references-column-count references-column-count-2" style="-moz-column-count: 2; -webkit-column-count: 2; column-count: 2; list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><a href="/w/index.php?title=Norman_Johnson_(mathematician)&action=edit&redlink=1" class="new" title="Norman Johnson (mathematician)（页面不存在）">N.W. Johnson</a>: <i>Geometries and Transformations</i>, (2018) <style data-mw-deduplicate="TemplateStyles:r61200749">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}</style><a href="/wiki/%E5%9B%BD%E9%99%85%E6%A0%87%E5%87%86%E4%B9%A6%E5%8F%B7" title="国际标准书号">ISBN</a> <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-1-107-10340-5" title="Special:网络书源/978-1-107-10340-5">978-1-107-10340-5</a> Chapter 11: <i>Finite symmetry groups</i>, 11.1 Polytopes and Honeycombs, p.225</span> </li> <li id="cite_note-m-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-m_2-0"><sup><b>2.0</b></sup></a> <a href="#cite_ref-m_2-1"><sup><b>2.1</b></sup></a> <a href="#cite_ref-m_2-2"><sup><b>2.2</b></sup></a> <a href="#cite_ref-m_2-3"><sup><b>2.3</b></sup></a></span> <span class="reference-text"><cite id="CITEREFMatoušek2002" class="citation"><a href="/w/index.php?title=Ji%C5%99%C3%AD_Matou%C5%A1ek_(mathematician)&action=edit&redlink=1" class="new" title="Jiří Matoušek (mathematician)（页面不存在）">Matoušek, Jiří</a>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=0N5RVe5lKQUC&pg=PA86">Lectures in Discrete Geometry</a>, <a href="/wiki/Graduate_Texts_in_Mathematics" class="mw-redirect" title="Graduate Texts in Mathematics">Graduate Texts in Mathematics</a> <b>212</b>, Springer, 5.3 Faces of a Convex Polytope, p. 86, 2002 <span class="reference-accessdate"> [<span class="nowrap">2019-09-16</span>]</span>, （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20190610095148/https://books.google.com/books?id=0N5RVe5lKQUC&pg=PA86">存档</a>于2019-06-10）</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B6%AD%E9%9D%A2&rft.aufirst=Ji%C5%99%C3%AD&rft.aulast=Matou%C5%A1ek&rft.btitle=Lectures+in+Discrete+Geometry&rft.date=2002&rft.genre=book&rft.pages=5.3+Faces+of+a+Convex+Polytope%2C+p.+86&rft.pub=Springer&rft.series=Graduate+Texts+in+Mathematics&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D0N5RVe5lKQUC%26pg%3DPA86&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span>.</span> </li> <li id="cite_note-g-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-g_3-0"><sup><b>3.0</b></sup></a> <a href="#cite_ref-g_3-1"><sup><b>3.1</b></sup></a> <a href="#cite_ref-g_3-2"><sup><b>3.2</b></sup></a></span> <span class="reference-text"><cite id="CITEREFGrünbaum2003" class="citation"><a href="/w/index.php?title=Branko_Gr%C3%BCnbaum&action=edit&redlink=1" class="new" title="Branko Grünbaum（页面不存在）">Grünbaum, Branko</a>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ISHO86XJ1CsC&pg=PA17">Convex Polytopes</a>, Graduate Texts in Mathematics <b>221</b> 2nd, Springer: 17, 2003 <span class="reference-accessdate"> [<span class="nowrap">2019-09-16</span>]</span>, （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20131031083447/http://books.google.com/books?id=ISHO86XJ1CsC&pg=PA17">存档</a>于2013-10-31）</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B6%AD%E9%9D%A2&rft.aufirst=Branko&rft.aulast=Gr%C3%BCnbaum&rft.btitle=Convex+Polytopes&rft.date=2003&rft.edition=2nd&rft.genre=book&rft.pages=17&rft.pub=Springer&rft.series=Graduate+Texts+in+Mathematics&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DISHO86XJ1CsC%26pg%3DPA17&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span>.</span> </li> <li id="cite_note-z-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-z_4-0"><sup><b>4.0</b></sup></a> <a href="#cite_ref-z_4-1"><sup><b>4.1</b></sup></a> <a href="#cite_ref-z_4-2"><sup><b>4.2</b></sup></a> <a href="#cite_ref-z_4-3"><sup><b>4.3</b></sup></a> <a href="#cite_ref-z_4-4"><sup><b>4.4</b></sup></a></span> <span class="reference-text"><cite id="CITEREFZiegler1995" class="citation"><a href="/w/index.php?title=G%C3%BCnter_M._Ziegler&action=edit&redlink=1" class="new" title="Günter M. Ziegler（页面不存在）">Ziegler, Günter M.</a>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=xd25TXSSUcgC&pg=PA51">Lectures on Polytopes</a>, Graduate Texts in Mathematics <b>152</b>, Springer, Definition 2.1, p. 51, 1995 <span class="reference-accessdate"> [<span class="nowrap">2019-09-16</span>]</span>, （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20190612031449/https://books.google.com/books?id=xd25TXSSUcgC&pg=PA51">存档</a>于2019-06-12）</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B6%AD%E9%9D%A2&rft.aufirst=G%C3%BCnter+M.&rft.aulast=Ziegler&rft.btitle=Lectures+on+Polytopes&rft.date=1995&rft.genre=book&rft.pages=Definition+2.1%2C+p.+51&rft.pub=Springer&rft.series=Graduate+Texts+in+Mathematics&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dxd25TXSSUcgC%26pg%3DPA51&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span>.</span> </li> <li id="cite_note-MGZ-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-MGZ_5-0"><sup><b>5.0</b></sup></a> <a href="#cite_ref-MGZ_5-1"><sup><b>5.1</b></sup></a></span> <span class="reference-text"><a href="#CITEREFMatoušek2002">Matoušek (2002)</a><span class="error harv-error" style="display: none; font-size:100%"> harvtxt模板錯誤: 多個指向目標 (2個): CITEREFMatoušek2002 (<a href="/wiki/Category:%E5%90%AB%E6%9C%89%E5%93%88%E4%BD%9B%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE%E6%A0%BC%E5%BC%8F%E7%B3%BB%E5%88%97%E6%A8%A1%E6%9D%BF%E9%93%BE%E6%8E%A5%E6%8C%87%E5%90%91%E9%94%99%E8%AF%AF%E7%9A%84%E9%A1%B5%E9%9D%A2" title="Category:含有哈佛参考文献格式系列模板链接指向错误的页面">幫助</a>)</span><sup id="cite_ref-m_2-0" class="reference"><a href="#cite_note-m-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>, p. 87; <a href="#CITEREFGrünbaum2003">Grünbaum (2003)</a><sup id="cite_ref-g_3-0" class="reference"><a href="#cite_note-g-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>, p. 27; <a href="#CITEREFZiegler1995">Ziegler (1995)</a><sup id="cite_ref-z_4-0" class="reference"><a href="#cite_note-z-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>, p. 17.</span> </li> <li id="cite_note-Bridge_1974-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-Bridge_1974_6-0"><sup><b>6.0</b></sup></a> <a href="#cite_ref-Bridge_1974_6-1"><sup><b>6.1</b></sup></a></span> <span class="reference-text">Bridge, N.J. Facetting the dodecahedron, <i>Acta crystallographica</i> <b>A30</b> (1974), pp. 548–552.</span> </li> <li id="cite_note-Inchbald_2006-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-Inchbald_2006_7-0"><sup><b>7.0</b></sup></a> <a href="#cite_ref-Inchbald_2006_7-1"><sup><b>7.1</b></sup></a></span> <span class="reference-text">Inchbald, G. Facetting diagrams, <i>The mathematical gazette</i>, <b>90</b> (2006), pp. 253–261.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><cite id="CITEREFMatoušek2002" class="citation"><a href="/w/index.php?title=Ji%C5%99%C3%AD_Matou%C5%A1ek_(mathematician)&action=edit&redlink=1" class="new" title="Jiří Matoušek (mathematician)（页面不存在）">Matoušek, Jiří</a>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=0N5RVe5lKQUC&pg=PA86">Lectures in Discrete Geometry</a>, <a href="/wiki/Graduate_Texts_in_Mathematics" class="mw-redirect" title="Graduate Texts in Mathematics">Graduate Texts in Mathematics</a> <b>212</b>, Springer, 5.3 Faces of a Convex Polytope, p. 86, 2002 <span class="reference-accessdate"> [<span class="nowrap">2019-09-16</span>]</span>, （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20190610095148/https://books.google.com/books?id=0N5RVe5lKQUC&pg=PA86">存档</a>于2019-06-10）</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B6%AD%E9%9D%A2&rft.aufirst=Ji%C5%99%C3%AD&rft.aulast=Matou%C5%A1ek&rft.btitle=Lectures+in+Discrete+Geometry&rft.date=2002&rft.genre=book&rft.pages=5.3+Faces+of+a+Convex+Polytope%2C+p.+86&rft.pub=Springer&rft.series=Graduate+Texts+in+Mathematics&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D0N5RVe5lKQUC%26pg%3DPA86&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span>.</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><cite id="CITEREFDe_LoeraRambauSantos2010" class="citation"><a href="/w/index.php?title=Jes%C3%BAs_A._De_Loera&action=edit&redlink=1" class="new" title="Jesús A. De Loera（页面不存在）">De Loera, Jesús A.</a>; Rambau, Jörg; <a href="/w/index.php?title=Francisco_Santos_Leal&action=edit&redlink=1" class="new" title="Francisco Santos Leal（页面不存在）">Santos, Francisco</a>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=SxY1Xrr12DwC&pg=PA493">Triangulations: Structures for Algorithms and Applications</a>, Algorithms and Computation in Mathematics <b>25</b>, Springer: 493, 2010, <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/9783642129711" title="Special:网络书源/9783642129711"><span title="国际标准书号">ISBN</span> 9783642129711</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B6%AD%E9%9D%A2&rft.au=Rambau%2C+J%C3%B6rg&rft.au=Santos%2C+Francisco&rft.aufirst=Jes%C3%BAs+A.&rft.aulast=De+Loera&rft.btitle=Triangulations%3A+Structures+for+Algorithms+and+Applications&rft.date=2010&rft.genre=book&rft.isbn=9783642129711&rft.pages=493&rft.pub=Springer&rft.series=Algorithms+and+Computation+in+Mathematics&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DSxY1Xrr12DwC%26pg%3DPA493&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span>.</span> </li> <li id="cite_note-Regular_Polytopes_book-10"><span class="mw-cite-backlink">^ <a href="#cite_ref-Regular_Polytopes_book_10-0"><sup><b>10.0</b></sup></a> <a href="#cite_ref-Regular_Polytopes_book_10-1"><sup><b>10.1</b></sup></a></span> <span class="reference-text"><cite class="citation book"><a href="/wiki/%E5%93%88%E7%BD%97%E5%BE%B7%C2%B7%E6%96%AF%E7%A7%91%E7%89%B9%C2%B7%E9%BA%A6%E5%85%8B%E5%94%90%E7%BA%B3%C2%B7%E8%80%83%E5%85%8B%E6%96%AF%E7%89%B9" title="哈罗德·斯科特·麦克唐纳·考克斯特">H. S. M. Coxeter</a>. Regular Polytopes, Dover Books on Mathematics. Courier Corporation. 2012. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/9780486141589" title="Special:网络书源/9780486141589"><span title="国际标准书号">ISBN</span> 9780486141589</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B6%AD%E9%9D%A2&rft.au=H.+S.+M.+Coxeter&rft.btitle=Regular+Polytopes%2C+Dover+Books+on+Mathematics&rft.date=2012&rft.genre=book&rft.isbn=9780486141589&rft.pub=Courier+Corporation&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-article_johnson2003polytopes-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-article_johnson2003polytopes_11-0">^</a></b></span> <span class="reference-text"><cite class="citation web"><span class="ilh-all" data-orig-title="諾曼·詹森" data-lang-code="en" data-lang-name="英语" data-foreign-title="Norman Johnson (mathematician)"><span class="ilh-page"><a href="/w/index.php?title=%E8%AB%BE%E6%9B%BC%C2%B7%E8%A9%B9%E6%A3%AE&action=edit&redlink=1" class="new" title="諾曼·詹森（页面不存在）">Johnson, Norman</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Norman_Johnson_(mathematician)" class="extiw" title="en:Norman Johnson (mathematician)"><span lang="en" dir="auto">Norman Johnson (mathematician)</span></a></span><span class="ilh-paren">）</span></span></span>. <a rel="nofollow" class="external text" href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.694.8688&rep=rep1&type=pdf">Polytopes-abstract and real</a>. Citeseer. 2003 <span class="reference-accessdate"> [<span class="nowrap">2019-09-16</span>]</span>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20170305055635/http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.694.8688&rep=rep1&type=pdf">存档</a>于2017-03-05）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B6%AD%E9%9D%A2&rft.au=%3Cspan+class%3D%22ilh-all+%22+data-orig-title%3D%22%E8%AB%BE%E6%9B%BC%C2%B7%E8%A9%B9%E6%A3%AE%22+data-lang-code%3D%22en%22+data-lang-name%3D%22%E8%8B%B1%E8%AF%AD%22+data-foreign-title%3D%22Norman+Johnson+%28mathematician%29%22%3E%3Cspan+class%3D%22ilh-page%22%3EJohnson%2C+Norman%3C%2Fspan%3E%3Cspan+class%3D%22noprint+ilh-comment%22%3E%3Cspan+class%3D%22ilh-paren%22%3E%EF%BC%88%3C%2Fspan%3E%3Cspan+class%3D%22ilh-lang%22%3E%E8%8B%B1%E8%AF%AD%3C%2Fspan%3E%3Cspan+class%3D%22ilh-colon%22%3E%EF%BC%9A%3C%2Fspan%3E%3Cspan+class%3D%22ilh-link%22%3E-%7B%3Cspan+lang%3D%22en%22+dir%3D%22auto%22%3ENorman+Johnson+%28mathematician%29%3C%2Fspan%3E%7D-%3C%2Fspan%3E%3Cspan+class%3D%22ilh-paren%22%3E%EF%BC%89%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E&rft.btitle=Polytopes-abstract+and+real&rft.date=2003&rft.genre=unknown&rft.pub=Citeseer&rft_id=http%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fdownload%3Fdoi%3D10.1.1.694.8688%26rep%3Drep1%26type%3Dpdf&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-steelpillow_VertexFigures-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-steelpillow_VertexFigures_12-0">^</a></b></span> <span class="reference-text"><cite class="citation web">Guy Inchbald. <a rel="nofollow" class="external text" href="http://www.steelpillow.com/polyhedra/vertex_figures/VertexFigures.htm#complete">Vertex figures: The complete vertex and general vertex figures</a>. steelpillow. 2005-01-06 <span class="reference-accessdate"> [<span class="nowrap">2016-08-02</span>]</span>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20160819053502/http://www.steelpillow.com/polyhedra/vertex_figures/VertexFigures.htm#complete">存档</a>于2016-08-19）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B6%AD%E9%9D%A2&rft.au=Guy+Inchbald&rft.btitle=Vertex+figures%3A+The+complete+vertex+and+general+vertex+figures&rft.date=2005-01-06&rft.genre=unknown&rft.pub=steelpillow&rft_id=http%3A%2F%2Fwww.steelpillow.com%2Fpolyhedra%2Fvertex_figures%2FVertexFigures.htm%23complete&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-book_mcmullen2002abstract-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-book_mcmullen2002abstract_13-0"><sup><b>13.0</b></sup></a> <a href="#cite_ref-book_mcmullen2002abstract_13-1"><sup><b>13.1</b></sup></a></span> <span class="reference-text"><cite class="citation book">McMullen, P. and Schulte, E. <a rel="nofollow" class="external text" href="https://archive.org/details/abstractregularp0000mcmu">Abstract Regular Polytopes</a>. Abstract Regular Polytopes. Cambridge University Press. 2002. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/9780521814966" title="Special:网络书源/9780521814966"><span title="国际标准书号">ISBN</span> 9780521814966</a>. <a rel="nofollow" class="external text" href="http://lccn.loc.gov/02017391"><span title="美国国会图书馆控制码">LCCN 02017391</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B6%AD%E9%9D%A2&rft.au=McMullen%2C+P.+and+Schulte%2C+E.&rft.btitle=Abstract+Regular+Polytopes&rft.date=2002&rft.genre=book&rft.isbn=9780521814966&rft.pub=Cambridge+University+Press&rft.series=Abstract+Regular+Polytopes&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fabstractregularp0000mcmu&rft_id=info%3Alccn%2F02017391&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span> <span style="font-size:100%" class="error citation-comment"><code style="color:inherit; border:inherit; padding:inherit;">|number=</code>被忽略 (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#parameter_discarded" title="Help:引文格式1错误">帮助</a>)</span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><a href="/w/index.php?title=Norman_Johnson_(mathematician)&action=edit&redlink=1" class="new" title="Norman Johnson (mathematician)（页面不存在）">N.W. Johnson</a>: <i>Geometries and Transformations</i>, (2018) <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r61200749"><a href="/wiki/%E5%9B%BD%E9%99%85%E6%A0%87%E5%87%86%E4%B9%A6%E5%8F%B7" title="国际标准书号">ISBN</a> <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-1-107-10340-5" title="Special:网络书源/978-1-107-10340-5">978-1-107-10340-5</a> Chapter 11: <i>Finite Symmetry Groups</i>, 11.1 <i>Polytopes and Honeycombs</i>, p.226</span> </li> <li id="cite_note-Euclid-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-Euclid_15-0">^</a></b></span> <span class="reference-text"><cite class="citation book"><a href="/w/index.php?title=T._L._Heath&action=edit&redlink=1" class="new" title="T. L. Heath（页面不存在）">Heath, Thomas L.</a> <a rel="nofollow" class="external text" href="https://archive.org/details/nlsiu.513.hea-1.34462">The Thirteen Books of Euclid's Elements</a> 2nd ed. [Facsimile. Original publication: Cambridge University Press, 1925]. New York: Dover Publications. 1956.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B6%AD%E9%9D%A2&rft.aufirst=Thomas+L.&rft.aulast=Heath&rft.btitle=The+Thirteen+Books+of+Euclid%27s+Elements&rft.date=1956&rft.edition=2nd+ed.+%5BFacsimile.+Original+publication%3A+Cambridge+University+Press%2C+1925%5D&rft.genre=book&rft.place=New+York&rft.pub=Dover+Publications&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fnlsiu.513.hea-1.34462&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span> <dl><dd>(3 vols.): <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r61200749"><a href="/wiki/%E5%9B%BD%E9%99%85%E6%A0%87%E5%87%86%E4%B9%A6%E5%8F%B7" title="国际标准书号">ISBN</a> <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0-486-60088-2" title="Special:网络书源/0-486-60088-2">0-486-60088-2</a> (vol. 1), <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r61200749"><a href="/wiki/%E5%9B%BD%E9%99%85%E6%A0%87%E5%87%86%E4%B9%A6%E5%8F%B7" title="国际标准书号">ISBN</a> <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0-486-60089-0" title="Special:网络书源/0-486-60089-0">0-486-60089-0</a> (vol. 2), <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r61200749"><a href="/wiki/%E5%9B%BD%E9%99%85%E6%A0%87%E5%87%86%E4%B9%A6%E5%8F%B7" title="国际标准书号">ISBN</a> <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0-486-60090-4" title="Special:网络书源/0-486-60090-4">0-486-60090-4</a> (vol. 3).</dd></dl> </span></li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><cite id="CITEREFWenninger1974" class="citation">Wenninger, Magnus J., <a rel="nofollow" class="external text" href="https://books.google.com/books?id=N8lX2T-4njIC&pg=PA1">Polyhedron Models</a>, Cambridge University Press: 1, 1974 <span class="reference-accessdate"> [<span class="nowrap">2019-09-16</span>]</span>, <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/9780521098595" title="Special:网络书源/9780521098595"><span title="国际标准书号">ISBN</span> 9780521098595</a>, （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20150321164201/http://books.google.com/books?id=N8lX2T-4njIC&pg=PA1">存档</a>于2015-03-21）</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B6%AD%E9%9D%A2&rft.aufirst=Magnus+J.&rft.aulast=Wenninger&rft.btitle=Polyhedron+Models&rft.date=1974&rft.genre=book&rft.isbn=9780521098595&rft.pages=1&rft.pub=Cambridge+University+Press&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DN8lX2T-4njIC%26pg%3DPA1&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span>.</span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><cite id="CITEREFCromwell1999" class="citation">Cromwell, Peter R., <a rel="nofollow" class="external text" href="https://books.google.com/books?id=OJowej1QWpoC&pg=PA13">Polyhedra</a>, Cambridge University Press: 13, 1999 <span class="reference-accessdate"> [<span class="nowrap">2019-09-16</span>]</span>, （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20190613063855/https://books.google.com/books?id=OJowej1QWpoC&pg=PA13">存档</a>于2019-06-13）</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B6%AD%E9%9D%A2&rft.aufirst=Peter+R.&rft.aulast=Cromwell&rft.btitle=Polyhedra&rft.date=1999&rft.genre=book&rft.pages=13&rft.pub=Cambridge+University+Press&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DOJowej1QWpoC%26pg%3DPA13&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Mathworld_Cell-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-Mathworld_Cell_18-0">^</a></b></span> <span class="reference-text"><cite class="citation web"><a href="/wiki/%E5%9F%83%E9%87%8C%E5%85%8B%C2%B7%E9%9F%A6%E6%96%AF%E5%9D%A6%E5%9B%A0" title="埃里克·韦斯坦因">Weisstein, Eric W.</a> (编). <a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/Cell.html">Cell</a>. at <a href="/wiki/MathWorld" title="MathWorld"><i>MathWorld</i></a>--A Wolfram Web Resource. <a href="/wiki/%E6%B2%83%E5%B0%94%E5%A4%AB%E5%8B%92%E5%A7%86%E7%A0%94%E7%A9%B6%E5%85%AC%E5%8F%B8" title="沃尔夫勒姆研究公司">Wolfram Research, Inc.</a> <span style="font-family: sans-serif; cursor: default; color:var(--color-subtle, #54595d); font-size: 0.8em; bottom: 0.1em; font-weight: bold;" title="连接到英语网页">（英语）</span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B6%AD%E9%9D%A2&rft.atitle=Cell&rft.aufirst=Eric+W.&rft.aulast=Weisstein&rft.genre=unknown&rft.jtitle=at+%27%27MathWorld%27%27--A+Wolfram+Web+Resource&rft_id=http%3A%2F%2Fmathworld.wolfram.com%2FCell.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="http://www.steelpillow.com/polyhedra/ditela.html">Ditela, polytopes and dyads</a>. <span class="reference-accessdate"> [<span class="nowrap">2019-09-16</span>]</span>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20181018090730/http://www.steelpillow.com/polyhedra/ditela.html">存档</a>于2018-10-18）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B6%AD%E9%9D%A2&rft.btitle=Ditela%2C+polytopes+and+dyads&rft.genre=unknown&rft_id=http%3A%2F%2Fwww.steelpillow.com%2Fpolyhedra%2Fditela.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-article_施开达1999正则多胞形和-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-article_施开达1999正则多胞形和_20-0">^</a></b></span> <span class="reference-text"><cite class="citation journal">施开达, 马利庄. 正则多胞形和 N 维空间有限旋转群理论的一些新结果. 自然科学进展: 国家重点实验室通讯. 1999, <b>9</b> (A12): 1336––1341.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B6%AD%E9%9D%A2&rft.atitle=%E6%AD%A3%E5%88%99%E5%A4%9A%E8%83%9E%E5%BD%A2%E5%92%8C+N+%E7%BB%B4%E7%A9%BA%E9%97%B4%E6%9C%89%E9%99%90%E6%97%8B%E8%BD%AC%E7%BE%A4%E7%90%86%E8%AE%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E6%96%B0%E7%BB%93%E6%9E%9C&rft.au=%E6%96%BD%E5%BC%80%E8%BE%BE%2C+%E9%A9%AC%E5%88%A9%E5%BA%84&rft.date=1999&rft.genre=article&rft.issue=A12&rft.jtitle=%E8%87%AA%E7%84%B6%E7%A7%91%E5%AD%A6%E8%BF%9B%E5%B1%95%3A+%E5%9B%BD%E5%AE%B6%E9%87%8D%E7%82%B9%E5%AE%9E%E9%AA%8C%E5%AE%A4%E9%80%9A%E8%AE%AF&rft.pages=1336--1341&rft.volume=9&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-article_araujo2013colorful-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-article_araujo2013colorful_21-0">^</a></b></span> <span class="reference-text"><cite class="citation journal">Araujo-Pardo, Gabriela and Hubard, Isabel and Oliveros, Deborah and Schulte, Egon. Colorful polytopes and graphs. Israel Journal of Mathematics (Springer). 2013, <b>195</b> (2): 647––675.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B6%AD%E9%9D%A2&rft.atitle=Colorful+polytopes+and+graphs&rft.au=Araujo-Pardo%2C+Gabriela+and+Hubard%2C+Isabel+and+Oliveros%2C+Deborah+and+Schulte%2C+Egon&rft.date=2013&rft.genre=article&rft.issue=2&rft.jtitle=Israel+Journal+of+Mathematics&rft.pages=647--675&rft.volume=195&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-MZ-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-MZ_22-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMatoušek2002">Matoušek (2002)</a><span class="error harv-error" style="display: none; font-size:100%"> harvtxt模板錯誤: 多個指向目標 (2個): CITEREFMatoušek2002 (<a href="/wiki/Category:%E5%90%AB%E6%9C%89%E5%93%88%E4%BD%9B%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE%E6%A0%BC%E5%BC%8F%E7%B3%BB%E5%88%97%E6%A8%A1%E6%9D%BF%E9%93%BE%E6%8E%A5%E6%8C%87%E5%90%91%E9%94%99%E8%AF%AF%E7%9A%84%E9%A1%B5%E9%9D%A2" title="Category:含有哈佛参考文献格式系列模板链接指向错误的页面">幫助</a>)</span><sup id="cite_ref-m_2-3" class="reference"><a href="#cite_note-m-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>, p. 87; <a href="#CITEREFZiegler1995">Ziegler (1995)</a><sup id="cite_ref-z_4-4" class="reference"><a href="#cite_note-z-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>, p. 71.</span> </li> <li id="cite_note-article_nishio2017describing-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-article_nishio2017describing_23-0">^</a></b></span> <span class="reference-text"><cite class="citation journal">Nishio, Kengo and Miyazaki, Takehide. Describing polyhedral tilings and higher dimensional polytopes by sequence of their two-dimensional components. Scientific reports (Nature Publishing Group). 2017, <b>7</b>: 40269.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B6%AD%E9%9D%A2&rft.atitle=Describing+polyhedral+tilings+and+higher+dimensional+polytopes+by+sequence+of+their+two-dimensional+components&rft.au=Nishio%2C+Kengo+and+Miyazaki%2C+Takehide&rft.date=2017&rft.genre=article&rft.jtitle=Scientific+reports&rft.pages=40269&rft.volume=7&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="外部連結"><span id=".E5.A4.96.E9.83.A8.E9.80.A3.E7.B5.90"></span>外部連結</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B6%AD%E9%9D%A2&action=edit&section=17" title="编辑章节：外部連結"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="citation mathworld" id="Reference-Mathworld-多維面"><cite class="citation web"><a href="/wiki/%E5%9F%83%E9%87%8C%E5%85%8B%C2%B7%E9%9F%A6%E6%96%AF%E5%9D%A6%E5%9B%A0" title="埃里克·韦斯坦因">埃里克·韦斯坦因</a>. <a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/Face.html">多維面</a>. <a href="/wiki/MathWorld" title="MathWorld">MathWorld</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B6%AD%E9%9D%A2&rft.atitle=%E5%A4%9A%E7%B6%AD%E9%9D%A2&rft.au=%E5%9F%83%E9%87%8C%E5%85%8B%C2%B7%E9%9F%A6%E6%96%AF%E5%9D%A6%E5%9B%A0&rft.genre=unknown&rft.jtitle=MathWorld&rft_id=http%3A%2F%2Fmathworld.wolfram.com%2FFace.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span></li> <li><span class="citation mathworld" id="Reference-Mathworld-維面"><cite class="citation web"><a href="/wiki/%E5%9F%83%E9%87%8C%E5%85%8B%C2%B7%E9%9F%A6%E6%96%AF%E5%9D%A6%E5%9B%A0" title="埃里克·韦斯坦因">埃里克·韦斯坦因</a>. <a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/Facet.html">維面</a>. <a href="/wiki/MathWorld" title="MathWorld">MathWorld</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%B6%AD%E9%9D%A2&rft.atitle=%E7%B6%AD%E9%9D%A2&rft.au=%E5%9F%83%E9%87%8C%E5%85%8B%C2%B7%E9%9F%A6%E6%96%AF%E5%9D%A6%E5%9B%A0&rft.genre=unknown&rft.jtitle=MathWorld&rft_id=http%3A%2F%2Fmathworld.wolfram.com%2FFacet.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r84265675">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl 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href="/w/index.php?title=%E5%89%AF%E6%B3%95%E7%B7%9A&action=edit&redlink=1" class="new" title="副法線（页面不存在）">副法線</a></li> <li><a href="/wiki/%E6%9B%B2%E7%BA%BF" title="曲线">曲线</a></li> <li><a href="/wiki/%E5%9C%86%E9%94%A5%E6%9B%B2%E7%BA%BF" title="圆锥曲线">圆锥曲线</a></li> <li><a href="/wiki/%E5%8F%8C%E6%9B%B2%E7%BA%BF" title="双曲线">双曲线</a></li> <li><a href="/wiki/%E6%8A%9B%E7%89%A9%E7%BA%BF" title="抛物线">抛物线</a></li> <li><a href="/wiki/%E6%AD%A3%E5%BC%A6%E6%9B%B2%E7%B7%9A" title="正弦曲線">正弦曲線</a></li> <li><a href="/wiki/%E8%9A%8C%E7%BA%BF" title="蚌线">蚌线</a></li> <li><a href="/wiki/%E8%9C%97%E7%BA%BF" class="mw-redirect" title="蜗线">蜗线</a></li> <li><a href="/wiki/%E8%9E%BA%E7%BA%BF" title="螺线">螺线</a>（<a href="/wiki/%E9%98%BF%E5%9F%BA%E7%B1%B3%E5%BE%B7%E8%9E%BA%E7%BA%BF" title="阿基米德螺线">阿基米德螺线</a>、<a href="/wiki/%E7%AD%89%E8%A7%92%E8%9E%BA%E7%BA%BF" title="等角螺线">等角螺线</a>……）</li> <li><a href="/wiki/%E6%91%86%E7%BA%BF" title="摆线">摆线</a>（<a href="/wiki/%E6%9C%80%E9%80%9F%E9%99%8D%E7%B7%9A%E5%95%8F%E9%A1%8C" title="最速降線問題">最速降線問題</a>）</li> <li><a href="/wiki/%E6%82%AC%E9%93%BE%E7%BA%BF" title="悬链线">悬链线</a></li> <li><a href="/wiki/%E6%9B%B3%E7%89%A9%E7%BA%BF" title="曳物线">曳物线</a></li> <li><a href="/wiki/%E6%BC%B8%E4%BC%B8%E7%B7%9A" title="漸伸線">漸開線</a></li> <li><a href="/wiki/%E6%B8%90%E5%B1%88%E7%BA%BF" title="渐屈线">渐屈线</a></li> <li><a href="/wiki/%E6%B8%90%E8%BF%91%E7%BA%BF" title="渐近线">渐近线</a></li> <li><a href="/wiki/%E6%B5%8B%E5%9C%B0%E7%BA%BF" title="测地线">测地线</a></li> <li><a href="/wiki/%E9%82%8A_(%E5%B9%BE%E4%BD%95)" title="邊 (幾何)">邊</a></li> <li><a href="/wiki/%E5%91%A8%E9%95%BF" title="周长">周界</a></li> <li><a href="/wiki/%E5%BC%A6_(%E5%B9%BE%E4%BD%95)" title="弦 (幾何)">弦</a></li> <li><a href="/wiki/%E5%BC%A7" title="弧">弧</a></li> <li><a href="/wiki/%E7%9F%A2_(%E5%B9%BE%E4%BD%95)" title="矢 (幾何)">矢</a></li> <li><a href="/wiki/%E5%9E%82%E7%9B%B4%E5%B9%B3%E5%88%86%E7%B7%9A" title="垂直平分線">垂直平分線</a></li> <li><a href="/wiki/%E4%BB%A3%E6%95%B8%E6%9B%B2%E7%B7%9A" title="代數曲線">代數曲線</a></li> <li><a href="/wiki/%E6%A4%AD%E5%9C%86%E6%9B%B2%E7%BA%BF" title="椭圆曲线">椭圆曲线</a></li> <li><a href="/wiki/%E8%B6%85%E6%A9%A2%E5%9C%93" title="超橢圓">超橢圓</a></li> <li><a href="/wiki/%E6%98%9F%E5%BD%A2%E7%BA%BF" title="星形线">星形线</a></li> <li><a href="/wiki/%E4%B8%89%E5%B0%96%E7%93%A3%E7%BA%BF" title="三尖瓣线">三尖瓣线</a></li> <li><a href="/wiki/%E6%96%B9%E5%9C%93%E5%BD%A2" title="方圓形">方圓形</a></li> <li><a href="/wiki/%E5%8B%92%E6%B4%9B%E4%B8%89%E8%A7%92%E5%BD%A2" title="勒洛三角形">勒洛三角形</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: right;"><a href="/wiki/%E5%B9%B3%E9%9D%A2_(%E6%95%B0%E5%AD%A6)" title="平面 (数学)">平面</a>圖形</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%9C%86" title="圆">圆</a>（<a href="/wiki/%E5%B9%BF%E4%B9%89%E5%9C%86" title="广义圆">广义圆</a>）</li> <li><a href="/wiki/%E6%A4%AD%E5%9C%86" title="椭圆">椭圆</a></li> <li><a href="/wiki/%E6%89%87%E5%BD%A2" title="扇形">扇形</a></li> <li><a href="/wiki/%E5%BC%93%E5%BD%A2" title="弓形">弓形</a></li> <li><a href="/wiki/%E7%8E%AF%E5%BD%A2" title="环形">环形</a></li> <li><a href="/wiki/%E5%A4%9A%E8%BE%B9%E5%BD%A2" title="多边形">多边形</a></li> <li><a href="/wiki/%E4%B8%89%E8%A7%92%E5%BD%A2" title="三角形">三角形</a></li> <li><a href="/wiki/%E5%9B%9B%E9%82%8A%E5%BD%A2" title="四邊形">四邊形</a></li> <li><a href="/wiki/%E4%BA%94%E8%BE%B9%E5%BD%A2" title="五边形">五边形</a></li> <li><a href="/wiki/%E5%85%AD%E8%BE%B9%E5%BD%A2" title="六边形">六边形</a></li> <li><a href="/wiki/%E5%A4%9A%E8%BE%B9%E5%BD%A2" title="多边形">多边形</a></li> <li><a href="/wiki/%E6%AD%A3%E5%A4%9A%E8%BE%B9%E5%BD%A2" title="正多边形">正多边形</a></li> <li><a href="/wiki/%E6%A2%AF%E5%BD%A2" title="梯形">梯形</a></li> <li><a href="/wiki/%E5%B9%B3%E8%A1%8C%E5%9B%9B%E8%BE%B9%E5%BD%A2" title="平行四边形">平行四边形</a></li> <li><a href="/wiki/%E8%8F%B1%E5%BD%A2" title="菱形">菱形</a></li> <li><a href="/wiki/%E7%9F%A9%E5%BD%A2" title="矩形">矩形</a></li> <li><a href="/wiki/%E6%AD%A3%E6%96%B9%E5%BD%A2" title="正方形">正方形</a></li> <li><a href="/wiki/%E9%B7%82%E5%BD%A2" title="鷂形">鷂形</a></li> <li><a href="/wiki/%E5%8D%B5%E5%BD%A2%E7%BA%BF" title="卵形线">卵形线</a></li> <li><a href="/wiki/%E7%B4%A1%E9%8C%98%E5%BD%A2" title="紡錘形">梭形</a></li> <li><a href="/wiki/%E6%98%9F%E5%BD%A2%E5%A4%9A%E9%82%8A%E5%BD%A2" title="星形多邊形">星形</a></li> <li><a href="/wiki/%E4%BA%94%E8%A7%92%E6%98%9F" title="五角星">五角星</a></li> <li><a href="/wiki/%E5%85%AD%E8%A7%92%E6%98%9F" title="六角星">六角星</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: right;"><a href="/wiki/%E4%B8%89%E7%B6%AD%E7%A9%BA%E9%96%93" title="三維空間">立體</a>圖形</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%A4%9A%E9%9D%A2%E4%BD%93" title="多面体">多面体</a></li> <li><a href="/wiki/%E6%9F%8F%E6%8B%89%E5%9C%96%E7%AB%8B%E9%AB%94" title="柏拉圖立體">正多面體</a></li> <li><a href="/wiki/%E5%9B%9B%E9%9D%A2%E9%AB%94" title="四面體">四面體</a></li> <li><a href="/wiki/%E9%95%B7%E6%96%B9%E9%AB%94" title="長方體">長方體</a></li> <li><a href="/wiki/%E7%AB%8B%E6%96%B9%E9%AB%94" title="立方體">立方體</a></li> <li><a href="/wiki/%E5%B9%B3%E8%A1%8C%E5%85%AD%E9%9D%A2%E4%BD%93" title="平行六面体">平行六面体</a></li> <li><a href="/wiki/%E6%A3%B1%E6%9F%B1" title="棱柱">棱柱</a></li> <li><a href="/wiki/%E5%8F%8D%E6%A3%B1%E6%9F%B1" title="反棱柱">反棱柱</a></li> <li><a href="/wiki/%E6%A3%B1%E9%94%A5" title="棱锥">棱锥</a></li> <li><a href="/wiki/%E9%94%A5%E5%8F%B0" title="锥台">棱台</a></li> <li><a href="/wiki/%E5%9C%86%E6%9F%B1%E4%BD%93" title="圆柱体">圆柱体</a></li> <li><a href="/wiki/%E5%9C%86%E9%94%A5" title="圆锥">圆锥</a></li> <li><a href="/wiki/%E5%9C%86%E5%8F%B0" title="圆台">圆台</a></li> <li><a href="/wiki/%E6%A4%AD%E7%90%83" title="椭球">椭球</a>（<a href="/wiki/%E9%A1%9E%E7%90%83%E9%9D%A2" title="類球面">長球體</a>、<a href="/wiki/%E9%A1%9E%E7%90%83%E9%9D%A2" title="類球面">扁球體</a>）</li> <li><a href="/wiki/%E7%90%83_(%E6%95%B0%E5%AD%A6)" title="球 (数学)">球體</a></li> <li><a href="/wiki/%E7%90%83%E7%BC%BA" title="球缺">球缺</a></li> <li><a href="/wiki/%E7%90%83%E5%86%A0" title="球冠">球冠</a></li> <li><a href="/wiki/%E7%90%83%E5%8F%B0" title="球台">球台</a></li> <li><a href="/wiki/%E9%9B%A2%E5%BF%83%E7%8E%87" title="離心率">準線</a></li> <li><a href="/w/index.php?title=%E6%AF%8D%E7%BA%BF_(%E5%87%A0%E4%BD%95)&action=edit&redlink=1" class="new" title="母线 (几何)（页面不存在）">母線</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: right;"><a href="/wiki/%E6%9B%B2%E9%9D%A2" title="曲面">曲面</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E4%BA%8C%E6%AC%A1%E6%9B%B2%E9%9D%A2" title="二次曲面">二次曲面</a></li> <li><a href="/wiki/%E6%97%8B%E8%BD%89%E6%9B%B2%E9%9D%A2" title="旋轉曲面">旋轉曲面</a></li> <li><a href="/wiki/%E6%8A%9B%E7%89%A9%E9%9D%A2" title="抛物面">抛物面</a></li> <li><a href="/wiki/%E9%9B%99%E6%9B%B2%E9%9D%A2" title="雙曲面">雙曲面</a></li> <li><a href="/w/index.php?title=%E9%A9%AC%E9%9E%8D%E9%9D%A2&action=edit&redlink=1" class="new" title="马鞍面（页面不存在）">马鞍面</a></li> <li><a href="/wiki/%E7%90%83%E9%9D%A2" title="球面">球面</a></li> <li><a href="/wiki/%E6%A4%AD%E7%90%83" title="椭球">橢球面</a></li> <li><a href="/wiki/%E9%A1%9E%E7%90%83%E9%9D%A2" title="類球面">類球面</a></li> <li><a href="/wiki/%E7%8E%AF%E9%9D%A2" title="环面">环面</a></li> <li><a href="/wiki/%E8%8E%AB%E6%AF%94%E4%B9%8C%E6%96%AF%E5%B8%A6" title="莫比乌斯带">莫比乌斯带</a></li> <li><a href="/wiki/%E6%B5%81%E5%BD%A2" title="流形">流形</a></li> <li><a href="/wiki/%E9%BB%8E%E6%9B%BC%E6%9B%B2%E9%9D%A2" title="黎曼曲面">黎曼曲面</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: right;">高維空間</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%B6%85%E5%B9%B3%E9%9D%A2" title="超平面">超平面</a></li> <li><a class="mw-selflink selflink">超面</a></li> <li><a href="/wiki/%E8%B6%85%E6%9B%B2%E9%9D%A2" title="超曲面">超曲面</a></li> <li><a href="/wiki/%E8%83%9E_(%E7%B5%90%E6%A7%8B)" title="胞 (結構)">胞</a></li> <li><a href="/wiki/%E5%A4%9A%E8%83%9E%E5%BD%A2" title="多胞形">多胞形</a></li> <li><a href="/wiki/%E8%B6%85%E7%90%83%E9%9D%A2" title="超球面">超球體</a></li> <li><a href="/wiki/%E8%B6%85%E6%96%B9%E5%BD%A2" title="超方形">超方形</a></li> <li><a href="/wiki/%E5%9B%9B%E7%B6%AD%E8%B6%85%E6%AD%A3%E6%96%B9%E9%AB%94" title="四維超正方體">超立方體</a></li> <li><a href="/wiki/%E5%85%8B%E8%8E%B1%E5%9B%A0%E7%93%B6" title="克莱因瓶">克莱因瓶</a></li> <li><a href="/wiki/%E5%9B%9B%E7%B6%AD%E6%9F%B1%E9%AB%94%E6%9F%B1" title="四維柱體柱">四維柱體柱</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: right;">圖形關係</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%9B%B8%E4%BC%BC_(%E5%B9%BE%E4%BD%95)" title="相似 (幾何)">相似</a></li> <li><a href="/wiki/%E5%85%A8%E7%AD%89" title="全等">全等</a></li> <li><a href="/wiki/%E5%B0%8D%E7%A8%B1" title="對稱">對稱</a></li> <li><a href="/wiki/%E5%B9%B3%E8%A1%8C" title="平行">平行</a></li> <li><a href="/wiki/%E5%9E%82%E7%9B%B4" title="垂直">垂直</a></li> <li><a href="/wiki/%E7%9B%B8%E4%BA%A4" title="相交">相交</a></li> <li><a href="/wiki/%E5%88%87%E7%BA%BF" title="切线">相切</a></li> <li><a href="/w/index.php?title=%E7%9B%B8%E9%9B%A2&action=edit&redlink=1" class="new" title="相離（页面不存在）">相離</a></li> <li><a href="/wiki/%E9%95%9C%E5%83%8F_(%E5%87%A0%E4%BD%95)" title="镜像 (几何)">镜像</a></li> <li><a href="/wiki/%E6%97%8B%E8%BD%AC" title="旋转">旋转</a></li> <li><a href="/wiki/%E5%8F%8D%E6%BC%94" title="反演">反演</a></li> <li><a href="/wiki/%E6%88%AA%E9%9D%A2_(%E5%B9%BE%E4%BD%95)" title="截面 (幾何)">截面</a></li> <li><a href="/wiki/%E7%BC%A9%E6%94%BE" title="缩放">缩放</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: right;"><a href="/wiki/%E4%B8%89%E8%A7%92%E5%BD%A2" title="三角形">三角形</a>關係</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%9B%B8%E4%BC%BC%E4%B8%89%E8%A7%92%E5%BD%A2" title="相似三角形">相似三角形</a></li> <li><a href="/wiki/%E5%85%A8%E7%AD%89%E4%B8%89%E8%A7%92%E5%BD%A2" title="全等三角形">全等三角形</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: right;"><a href="/wiki/%E9%87%8F_(%E6%95%B0%E5%AD%A6)" title="量 (数学)">量</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%B7%9D%E7%A6%BB" title="距离">距离</a></li> <li><a href="/wiki/%E9%95%BF%E5%BA%A6" title="长度">长度</a></li> <li><a href="/wiki/%E5%91%A8%E9%95%BF" title="周长">周长</a></li> <li><a href="/wiki/%E5%BC%A7%E9%95%BF" title="弧长">弧长</a></li> <li><a href="/wiki/%E9%AB%98%E5%BA%A6" title="高度">高度</a></li> <li><a href="/wiki/%E9%9D%A2%E7%A7%AF" title="面积">面积</a></li> <li><a href="/wiki/%E8%A1%A8%E9%9D%A2%E7%A9%8D" title="表面積">表面積</a></li> <li><a href="/wiki/%E4%BD%93%E7%A7%AF" title="体积">体积</a></li> <li><a href="/wiki/%E5%AE%B9%E7%A9%8D" class="mw-redirect" title="容積">容積</a></li> <li><a href="/wiki/%E5%BA%A6_(%E8%A7%92)" title="度 (角)">角度</a></li> <li><a href="/wiki/%E6%9B%B2%E7%8E%87" title="曲率">曲率</a></li> <li><a href="/wiki/%E6%9B%B2%E7%BA%BF%E7%9A%84%E6%8C%A0%E7%8E%87" title="曲线的挠率">撓率</a></li> <li><a href="/wiki/%E9%9B%A2%E5%BF%83%E7%8E%87" title="離心率">離心率</a></li> <li><a href="/wiki/%E5%87%B9%E5%87%B8%E6%80%A7_(%E5%B9%BE%E4%BD%95)" title="凹凸性 (幾何)">凹凸性</a></li> <li><a href="/w/index.php?title=%E6%9C%89%E5%90%91%E6%9B%B2%E9%9D%A2&action=edit&redlink=1" class="new" title="有向曲面（页面不存在）">有向曲面</a></li> <li><a href="/wiki/%E5%8F%AF%E5%B1%95%E6%9B%B2%E9%9D%A2" title="可展曲面">可展曲面</a></li> <li><a href="/wiki/%E7%9B%B4%E7%B4%8B%E6%9B%B2%E9%9D%A2" title="直紋曲面">直紋曲面</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: right;">作圖</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%B0%BA" title="尺">尺</a> <ul><li><a href="/wiki/%E7%9B%B4%E5%B0%BA" title="直尺">直尺</a></li> <li><a href="/wiki/%E4%B8%89%E8%A7%92%E5%B0%BA" title="三角尺">三角尺</a></li></ul></li> <li><a href="/wiki/%E5%9C%86%E8%A7%84" title="圆规">圆规</a></li> <li><a href="/wiki/%E5%B0%BA%E8%A7%84%E4%BD%9C%E5%9B%BE" title="尺规作图">尺规作图</a></li> <li><a href="/wiki/%E4%BA%8C%E5%88%BB%E5%B0%BA%E4%BD%9C%E5%9C%96" title="二刻尺作圖">二刻尺作圖</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: right;">分支</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97%E5%87%A0%E4%BD%95" title="欧几里得几何">平面幾何</a></li> <li><a href="/wiki/%E7%AB%8B%E4%BD%93%E5%87%A0%E4%BD%95" title="立体几何">立体几何</a></li> <li><a href="/wiki/%E4%B8%89%E8%A7%92%E5%AD%A6" title="三角学">三角学</a></li> <li><a href="/wiki/%E8%A7%A3%E6%9E%90%E5%87%A0%E4%BD%95" title="解析几何">解析几何</a></li> <li><a href="/wiki/%E5%BE%AE%E5%88%86%E5%87%A0%E4%BD%95" title="微分几何">微分几何</a></li> <li><a href="/wiki/%E6%8B%93%E6%89%91%E5%AD%A6" title="拓扑学">拓扑学</a></li> <li><a href="/wiki/%E5%9B%BE%E8%AE%BA" title="图论">图论</a></li> <li><a href="/wiki/%E6%91%BA%E7%B4%99%E6%95%B8%E5%AD%B8" title="摺紙數學">摺紙數學</a></li> <li><a href="/wiki/%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97%E5%87%A0%E4%BD%95" title="欧几里得几何">欧几里得几何</a></li> <li><a href="/wiki/%E9%9D%9E%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97%E5%87%A0%E4%BD%95" title="非欧几里得几何">非欧几里得几何</a>（<a href="/wiki/%E5%8F%8C%E6%9B%B2%E5%87%A0%E4%BD%95" title="双曲几何">双曲几何</a>、<a href="/wiki/%E7%90%83%E9%9D%A2%E5%B9%BE%E4%BD%95%E5%AD%B8" title="球面幾何學">球面幾何</a>……）</li> <li><a href="/wiki/%E5%88%86%E5%BD%A2" title="分形">分形</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: right;">理論</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%AE%9A%E7%90%86" title="定理">定理</a></li> <li><a href="/wiki/%E5%85%AC%E7%90%86" title="公理">公理</a></li> <li><a href="/wiki/%E5%AE%9A%E4%B9%89" title="定义">定义</a></li> <li><a href="/wiki/%E6%95%B8%E5%AD%B8%E8%AD%89%E6%98%8E" title="數學證明">數學證明</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span typeof="mw:File"><span title="分类"><img alt="分类" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span><b><a href="/wiki/Category:%E5%87%A0%E4%BD%95%E5%AD%A6" title="Category:几何学">分类</a></b></li> <li><span typeof="mw:File"><span title="主题"><img alt="主题" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Symbol_portal_class.svg/16px-Symbol_portal_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Symbol_portal_class.svg/23px-Symbol_portal_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Symbol_portal_class.svg/31px-Symbol_portal_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span><b><a href="/wiki/Portal:%E5%87%A0%E4%BD%95%E5%AD%A6" title="Portal:几何学">主题</a></b></li> <li><span typeof="mw:File"><span title="共享资源页面"><img alt="共享资源页面" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span><b><a href="https://commons.wikimedia.org/wiki/Category:Geometry" class="extiw" title="commons:Category:Geometry">共享资源</a></b></li> <li><span typeof="mw:File"><span title="专题"><img alt="专题" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/16px-People_icon.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/24px-People_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/32px-People_icon.svg.png 2x" data-file-width="100" data-file-height="100" /></span></span><b><a href="/wiki/WikiProject:%E5%87%A0%E4%BD%95%E5%AD%A6" title="WikiProject:几何学">专题</a></b></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84261037"></div><div role="navigation" class="navbox" aria-labelledby="18px&#124;top_幾何形狀" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="collapsible-title navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84244141"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:%E5%B9%BE%E4%BD%95%E5%BD%A2%E7%8B%80" title="Template:幾何形狀"><abbr title="查看该模板">查</abbr></a></li><li class="nv-talk"><a href="/w/index.php?title=Template_talk:%E5%B9%BE%E4%BD%95%E5%BD%A2%E7%8B%80&action=edit&redlink=1" class="new" title="Template talk:幾何形狀（页面不存在）"><abbr title="讨论该模板">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:%E5%B9%BE%E4%BD%95%E5%BD%A2%E7%8B%80" title="Special:编辑页面/Template:幾何形狀"><abbr title="编辑该模板">编</abbr></a></li></ul></div><div id="18px&#124;top_幾何形狀" style="font-size:110%;margin:0 5em"><span class="mw-valign-top" typeof="mw:File"><a href="/wiki/File:Simple_pentagon.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Simple_pentagon.svg/18px-Simple_pentagon.svg.png" decoding="async" width="18" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Simple_pentagon.svg/27px-Simple_pentagon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/01/Simple_pentagon.svg/36px-Simple_pentagon.svg.png 2x" data-file-width="572" data-file-height="545" /></a></span> <a href="/wiki/%E5%87%A0%E4%BD%95%E5%BD%A2%E7%8A%B6" class="mw-redirect" title="几何形状">幾何形狀</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">分類</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">依對稱程度</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%AD%A3%E5%9C%96%E5%BD%A2" title="正圖形">正</a>（Regular）</li> <li><a href="/wiki/%E6%93%AC%E6%AD%A3%E5%A4%9A%E9%9D%A2%E9%AB%94" title="擬正多面體">擬正</a>（Quasiregular）</li> <li><span class="ilh-all" data-orig-title="半正圖形" data-lang-code="en" data-lang-name="英语" data-foreign-title="Semiregular_polytope"><span class="ilh-page"><a href="/w/index.php?title=%E5%8D%8A%E6%AD%A3%E5%9C%96%E5%BD%A2&action=edit&redlink=1" class="new" title="半正圖形（页面不存在）">半正</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Semiregular_polytope" class="extiw" title="en:Semiregular polytope"><span lang="en" dir="auto">Semiregular_polytope</span></a></span><span class="ilh-paren">）</span></span></span>（Semiregular）</li> <li><a href="/wiki/%E4%B8%8D%E5%AE%8C%E5%85%A8%E6%AD%A3%E9%91%B2%E5%B5%8C%E5%9C%96" title="不完全正鑲嵌圖">不完全正</a>（Demiregular）</li> <li><span class="ilh-all" data-orig-title="均勻圖形" data-lang-code="en" data-lang-name="英语" data-foreign-title="Uniform_polytope"><span class="ilh-page"><a href="/w/index.php?title=%E5%9D%87%E5%8B%BB%E5%9C%96%E5%BD%A2&action=edit&redlink=1" class="new" title="均勻圖形（页面不存在）">均勻</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Uniform_polytope" class="extiw" title="en:Uniform polytope"><span lang="en" dir="auto">Uniform_polytope</span></a></span><span class="ilh-paren">）</span></span></span>（Uniform）</li> <li><a href="/w/index.php?title=%E4%B8%8D%E8%A6%8F%E5%89%87%E5%9C%96%E5%BD%A2&action=edit&redlink=1" class="new" title="不規則圖形（页面不存在）">不規則</a>（Irregular）</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">依對稱性</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%AD%A3%E5%9C%96%E5%BD%A2" title="正圖形">正</a>（<a href="/wiki/%E6%A8%99%E8%A8%98_(%E5%B9%BE%E4%BD%95)" title="標記 (幾何)">標記</a>可遞）</li> <li><a href="/wiki/%E7%AD%89%E7%B6%AD%E9%9D%A2%E5%9C%96%E5%BD%A2" class="mw-redirect" title="等維面圖形">等維面</a>（<a class="mw-selflink selflink">維面</a>可遞）</li> <li><a href="/wiki/%E7%AD%89%E9%9D%A2%E5%9C%96%E5%BD%A2" title="等面圖形">等面</a>（<a href="/wiki/%E9%9D%A2_(%E5%B9%BE%E4%BD%95)" title="面 (幾何)">面</a>可遞）</li> <li><a href="/wiki/%E7%AD%89%E9%82%8A%E5%9C%96%E5%BD%A2" title="等邊圖形">等邊</a>（<a href="/wiki/%E9%82%8A_(%E5%B9%BE%E4%BD%95)" title="邊 (幾何)">邊</a>可遞）</li> <li><a href="/wiki/%E7%AD%89%E8%A7%92%E5%9C%96%E5%BD%A2" title="等角圖形">等角</a>（<a href="/wiki/%E9%A0%82%E9%BB%9E_(%E5%B9%BE%E4%BD%95)" title="頂點 (幾何)">點</a>可遞）</li> <li><a href="/wiki/%E7%AD%89%E9%9D%A2%E7%AD%89%E8%A7%92%E5%9C%96%E5%BD%A2" class="mw-redirect" title="等面等角圖形">等面等角</a>（<a href="/wiki/%E9%9D%A2_(%E5%B9%BE%E4%BD%95)" title="面 (幾何)">面</a>可遞且<a href="/wiki/%E9%A0%82%E9%BB%9E_(%E5%B9%BE%E4%BD%95)" title="頂點 (幾何)">點</a>可遞）</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">依<a href="/wiki/%E5%87%B9%E5%87%B8%E6%80%A7_(%E5%B9%BE%E4%BD%95)" title="凹凸性 (幾何)">凹凸性</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%87%B9%E5%87%B8%E6%80%A7_(%E5%B9%BE%E4%BD%95)#凸幾何圖形" title="凹凸性 (幾何)">凸</a></li> <li><a href="/wiki/%E5%87%B9%E5%87%B8%E6%80%A7_(%E5%B9%BE%E4%BD%95)#凹幾何圖形" title="凹凸性 (幾何)">非凸</a></li> <li><a href="/wiki/%E5%87%B9%E5%87%B8%E6%80%A7_(%E5%B9%BE%E4%BD%95)#凹幾何圖形" title="凹凸性 (幾何)">凹</a></li> <li><a href="/wiki/%E5%87%B9%E5%87%B8%E6%80%A7_(%E5%B9%BE%E4%BD%95)#星形幾何圖形" title="凹凸性 (幾何)">星形</a></li> <li><span class="ilh-all" data-orig-title="環狀多面體" data-lang-code="en" data-lang-name="英语" data-foreign-title="Toroidal_polyhedron"><span class="ilh-page"><a href="/w/index.php?title=%E7%92%B0%E7%8B%80%E5%A4%9A%E9%9D%A2%E9%AB%94&action=edit&redlink=1" class="new" title="環狀多面體（页面不存在）">環狀</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Toroidal_polyhedron" class="extiw" title="en:Toroidal polyhedron"><span lang="en" dir="auto">Toroidal_polyhedron</span></a></span><span class="ilh-paren">）</span></span></span></li> <li><a href="/wiki/%E6%89%AD%E6%AD%AA%E5%A4%9A%E9%9D%A2%E9%AB%94" title="扭歪多面體">扭歪</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">元素特性</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%B0%A1%E5%96%AE%E5%A4%9A%E8%83%9E%E5%BD%A2" title="簡單多胞形">簡單</a></li> <li><a href="/wiki/%E8%A4%87%E9%9B%9C%E5%A4%9A%E8%83%9E%E5%BD%A2" class="mw-redirect" title="複雜多胞形">複雜</a></li> <li><span class="ilh-all" data-orig-title="抽象多胞形" data-lang-code="en" data-lang-name="英语" data-foreign-title="abstract polytope"><span class="ilh-page"><a href="/w/index.php?title=%E6%8A%BD%E8%B1%A1%E5%A4%9A%E8%83%9E%E5%BD%A2&action=edit&redlink=1" class="new" title="抽象多胞形（页面不存在）">抽象</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/abstract_polytope" class="extiw" title="en:abstract polytope"><span lang="en" dir="auto">abstract polytope</span></a></span><span class="ilh-paren">）</span></span></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">所屬空間</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%AF%A6%E5%A4%9A%E8%83%9E%E5%BD%A2" class="mw-redirect" title="實多胞形">實數</a><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 \mathbb {R} ^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} ^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.897ex; height:2.343ex;" alt="{\displaystyle \mathbb {R} ^{n}}"></span></li> <li><a href="/wiki/%E8%A4%87%E5%A4%9A%E8%83%9E%E5%BD%A2" class="mw-redirect" title="複多胞形">複數</a><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 \mathbb {C} ^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {C} ^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a53b4e76242764d1bca004168353c380fef25258" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.897ex; height:2.343ex;" alt="{\displaystyle \mathbb {C} ^{n}}"></span></li> <li><span class="ilh-all" data-orig-title="四元多胞形" data-lang-code="en" data-lang-name="英语" data-foreign-title="Quaternionic polytope"><span class="ilh-page"><a href="/w/index.php?title=%E5%9B%9B%E5%85%83%E5%A4%9A%E8%83%9E%E5%BD%A2&action=edit&redlink=1" class="new" title="四元多胞形（页面不存在）">四元數</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Quaternionic_polytope" class="extiw" title="en:Quaternionic polytope"><span lang="en" dir="auto">Quaternionic polytope</span></a></span><span class="ilh-paren">）</span></span></span><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 \mathbb {Q} ^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Q} ^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce1121a4a9ff1c9f6b3e51008a1a1411b8f46231" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.027ex; height:2.676ex;" alt="{\displaystyle \mathbb {Q} ^{n}}"></span></li> <li><a href="/wiki/%E5%85%AB%E5%85%83%E5%A4%9A%E8%83%9E%E5%BD%A2" class="mw-redirect" title="八元多胞形">八元數</a><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 \mathbb {O} ^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">O</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {O} ^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c03e9f3b62d415777249a337a4c508cb69ee058" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.027ex; height:2.343ex;" alt="{\displaystyle \mathbb {O} ^{n}}"></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">維度</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%A4%9A%E8%83%9E%E5%BD%A2" title="多胞形">多胞形</a>（總稱）</li> <li><a href="/wiki/%E7%A9%BA%E5%A4%9A%E8%83%9E%E5%BD%A2" title="空多胞形">空多胞形</a>（<a href="/wiki/%E8%B2%A0%E7%B6%AD%E7%A9%BA%E9%96%93" title="負維空間">負維</a>）</li> <li><a href="/wiki/%E9%A0%82%E9%BB%9E_(%E5%B9%BE%E4%BD%95)" title="頂點 (幾何)">頂點</a>（<a href="/wiki/%E9%9B%B6%E7%B6%AD%E7%A9%BA%E9%96%93" title="零維空間">零維</a>）</li> <li><a href="/wiki/%E7%9B%B4%E7%BA%BF" title="直线">直线</a>（<a href="/wiki/%E4%B8%80%E7%BB%B4%E7%A9%BA%E9%97%B4" title="一维空间">一維</a>）</li> <li><a href="/wiki/%E5%A4%9A%E8%BE%B9%E5%BD%A2" title="多边形">多边形</a>（<a href="/wiki/%E4%BA%8C%E7%BB%B4%E7%A9%BA%E9%97%B4" title="二维空间">二維</a>）</li> <li><a href="/wiki/%E5%A4%9A%E9%9D%A2%E5%BD%A2" title="多面形">多面形</a>（<a href="/wiki/%E4%B8%89%E7%B6%AD%E7%A9%BA%E9%96%93" title="三維空間">三維</a>退化）</li> <li><a href="/wiki/%E5%A4%9A%E9%9D%A2%E4%BD%93" title="多面体">多面体</a>（<a href="/wiki/%E4%B8%89%E7%B6%AD%E7%A9%BA%E9%96%93" title="三維空間">三維</a>）</li> <li><a href="/wiki/%E5%A4%9A%E8%83%9E%E4%BD%93" class="mw-redirect" title="多胞体">多胞體</a> <ul><li><a href="/wiki/%E5%9B%9B%E7%B6%AD%E5%A4%9A%E8%83%9E%E9%AB%94" title="四維多胞體">四維多胞體</a></li> <li><a href="/wiki/%E4%BA%94%E7%B6%AD%E5%A4%9A%E8%83%9E%E9%AB%94" title="五維多胞體">五維多胞體</a></li></ul></li> <li><a href="/wiki/%E5%AF%86%E9%8B%AA" title="密鋪">密鋪</a></li> <li><a href="/wiki/%E9%91%B2%E5%B5%8C_(%E5%B9%BE%E4%BD%95)" title="鑲嵌 (幾何)">鑲嵌</a></li> <li><a href="/wiki/%E5%A0%86%E7%A0%8C" title="堆砌">堆砌</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px;background:#ddf;"><div style="padding:0em 0.25em">註：一般而言上面的分類皆可嵌套，例如「<a href="/wiki/%E6%98%9F%E5%BD%A2%E6%AD%A3%E5%A4%9A%E9%9D%A2%E9%AB%94" title="星形正多面體">正星形多面體</a>」（<a href="/wiki/%E6%AD%A3%E5%9C%96%E5%BD%A2" title="正圖形">正</a>+<a href="/wiki/%E5%87%B9%E5%87%B8%E6%80%A7_(%E5%B9%BE%E4%BD%95)#星形幾何圖形" title="凹凸性 (幾何)">星形</a>+<a href="/wiki/%E5%A4%9A%E9%9D%A2%E9%AB%94" class="mw-redirect" title="多面體">多面體</a>）</div></td></tr></tbody></table><div></div></td><td class="noviewer navbox-image" rowspan="3" style="width:1px;padding:0px 0px 0px 2px"><div><span typeof="mw:File"><a href="/wiki/File:Basic_shapes.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Basic_shapes.svg/100px-Basic_shapes.svg.png" decoding="async" width="100" height="72" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Basic_shapes.svg/150px-Basic_shapes.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/38/Basic_shapes.svg/200px-Basic_shapes.svg.png 2x" data-file-width="697" data-file-height="503" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">性質</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%9D%A2%E7%A7%AF" title="面积">面积</a></li> <li><a href="/wiki/%E4%BD%93%E7%A7%AF" title="体积">体积</a></li> <li><a href="/wiki/%E8%A1%A8%E9%9D%A2%E7%A9%8D" title="表面積">表面積</a></li> <li><a href="/wiki/%E5%86%85%E8%A7%92" title="内角">內角</a></li> <li><a href="/wiki/%E4%BA%8F%E6%A0%BC" title="亏格">虧格</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">組成</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a class="mw-selflink-fragment" href="#負一維面">極小面</a></li> <li><a href="/wiki/%E9%A0%82%E9%BB%9E_(%E5%B9%BE%E4%BD%95)" title="頂點 (幾何)">頂點</a></li> <li><a href="/wiki/%E9%82%8A_(%E5%B9%BE%E4%BD%95)" title="邊 (幾何)">邊</a></li> <li><a href="/wiki/%E9%9D%A2_(%E5%B9%BE%E4%BD%95)" title="面 (幾何)">面</a></li> <li><a href="/wiki/%E8%83%9E_(%E7%B5%90%E6%A7%8B)" title="胞 (結構)">胞</a></li> <li>...</li> <li><b>維峰</b>（<a href="#(n-3)維面">章節</a>）</li> <li><a href="/wiki/%E7%BB%B4%E8%84%8A" title="维脊">維脊</a></li> <li><a class="mw-selflink selflink">維面</a></li> <li><b>體</b>（<a href="#體">章節</a>）（極大面）</li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div>相關主題：<a href="/wiki/%E5%BD%A2%E7%8B%80" title="形狀">形狀</a></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" 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