Micron Document
<!DOCTYPE html>
<html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-0 vector-toc-not-available vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-0 skin-theme-clientpref-day vector-sticky-header-enabled" lang="de" dir="ltr"><head>
<meta charset="UTF-8">
<title>Triakisoktaeder</title>
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<link rel="icon" type="image/png" href="./_res_/favicon.png">
<link rel="canonical" href="https://de.wikipedia.org/wiki/Triakisoktaeder"> <link href="./_mw_/ext.3d.styles.css" rel="stylesheet" type="text/css">
<link href="./_mw_/ext.math.styles.css" rel="stylesheet" type="text/css">
<link href="./_mw_/ext.wikimediamessages.styles.css" rel="stylesheet" type="text/css">
<link href="./_mw_/skins.vector.icons.css" rel="stylesheet" type="text/css">
<link href="./_mw_/skins.vector.search.codex.styles.css" rel="stylesheet" type="text/css">
<link href="./_mw_/skins.vector.styles.css" rel="stylesheet" type="text/css">
<meta name="ResourceLoaderDynamicStyles" content="">
<link href="./_mw_/ext.gadget.citeRef.css" rel="stylesheet" type="text/css">
<link href="./_mw_/ext.gadget.defaultPlainlinks.css" rel="stylesheet" type="text/css">
<link href="./_mw_/ext.gadget.dewikiCommonHide.css" rel="stylesheet" type="text/css">
<link href="./_mw_/ext.gadget.dewikiCommonLayout.css" rel="stylesheet" type="text/css">
<link href="./_mw_/ext.gadget.dewikiCommonStyle.css" rel="stylesheet" type="text/css">
<link href="./_mw_/ext.gadget.dewikiDarkmode.css" rel="stylesheet" type="text/css">
<link href="./_mw_/ext.gadget.dewikiResponsive.css" rel="stylesheet" type="text/css">
<link href="./_mw_/ext.gadget.specialSearch.css" rel="stylesheet" type="text/css">
<link rel="stylesheet" type="text/css" href="./_mw_/site.styles.css">
<link rel="stylesheet" type="text/css" href="./_mw_/noscript.css">
<link rel="stylesheet" type="text/css" href="./_res_/footer.css">
<link rel="stylesheet" type="text/css" href="./_res_/vector-2022.css">
</head>
<body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Triakisoktaeder rootpage-Triakisoktaeder skin-vector-2022 action-view">
<div class="mw-page-container">
<div class="mw-page-container-inner">
<div class="mw-content-container">
<main id="content" class="mw-body">
<header class="mw-body-header vector-page-titlebar">
<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Triakisoktaeder</span></h1>
</header>
<a id="top"></a>
<div id="bodyContent" class="vector-body ve-init-mw-desktopArticleTarget-targetContainer" aria-labelledby="firstHeading" data-mw-ve-target-container="">
<div id="contentSub">
<div id="mw-content-subtitle"></div>
</div>
<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="de" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="de" dir="ltr">

<p>Das <b>Triakisoktaeder</b> ist ein <a href="Kr%C3%BCmmung" title="Krümmung">konvexes</a> <a href="Polyeder" title="Polyeder">Polyeder</a>, das sich aus 24 <a href="Gleichschenkliges_Dreieck" title="Gleichschenkliges Dreieck">gleichschenkligen Dreiecken</a> zusammensetzt und zu den <a href="Catalanischer_K%C3%B6rper" title="Catalanischer Körper">Catalanischen Körpern</a> zählt. Es ist der <a href="Dualit%C3%A4t_(Mathematik)#Dualität_von_Polytopen" title="Dualität (Mathematik)">duale Körper</a> zum <a href="Hexaederstumpf" title="Hexaederstumpf">Hexaederstumpf</a> und hat 14 Ecken sowie 36 Kanten.
</p>

<div class="mw-heading mw-heading2"><h2 id="Entstehung">Entstehung</h2></div>
<p>Werden auf die acht Begrenzungsflächen eines <a href="Oktaeder" title="Oktaeder">Oktaeders</a> (Kantenlänge <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>a</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle a}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ffd2487510aa438433a2579450ab2b3d557e5edc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}" loading="lazy"></span>) <a href="Pyramide_(Geometrie)" title="Pyramide (Geometrie)">Pyramiden</a> mit der Flankenlänge <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>b</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle b}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f11423fbb2e967f986e36804a8ae4271734917c3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}" loading="lazy"></span> aufgesetzt, entsteht ein Triakisoktaeder, sofern die Bedingung <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {a}{3}}{\sqrt {3}}<b<{\tfrac {a}{4}}{\sqrt {6}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="false" scriptlevel="0">
<mfrac>
<mi>a</mi>
<mn>3</mn>
</mfrac>
</mstyle>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>3</mn>
</msqrt>
</mrow>
<mo>&lt;</mo>
<mi>b</mi>
<mo>&lt;</mo>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="false" scriptlevel="0">
<mfrac>
<mi>a</mi>
<mn>4</mn>
</mfrac>
</mstyle>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>6</mn>
</msqrt>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\tfrac {a}{3}}{\sqrt {3}}&lt;b&lt;{\tfrac {a}{4}}{\sqrt {6}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9a08f61c1e84a156c26413301cf7abb977b17bd7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:16.803ex; height:3.509ex;" alt="{\displaystyle {\tfrac {a}{3}}{\sqrt {3}}<b<{\tfrac {a}{4}}{\sqrt {6}}}" loading="lazy"></span> erfüllt ist.
</p>
<ul><li>Für den zuvor genannten minimalen Wert von <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>b</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle b}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f11423fbb2e967f986e36804a8ae4271734917c3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}" loading="lazy"></span> haben die aufgesetzten Pyramiden die Höhe 0, sodass lediglich das Oktaeder mit der Kantenlänge <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>a</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle a}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ffd2487510aa438433a2579450ab2b3d557e5edc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}" loading="lazy"></span> übrig bleibt.</li>
<li>Das spezielle Triakisoktaeder mit gleichen Flächenwinkeln entsteht, wenn <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b=a\,(2-{\sqrt {2}})}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>b</mi>
<mo>=</mo>
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo>−<!-- − --></mo>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>2</mn>
</msqrt>
</mrow>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle b=a\,(2-{\sqrt {2}})}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2080ba8892c67f9e42c63c33b747832c83fcd88b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.623ex; height:3.176ex;" alt="{\displaystyle b=a\,(2-{\sqrt {2}})}" loading="lazy"></span> ist.</li>
<li>Nimmt <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>b</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle b}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f11423fbb2e967f986e36804a8ae4271734917c3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}" loading="lazy"></span> den o.&nbsp;g. maximalen Wert an, entartet das Triakisoktaeder zu einem <a href="Rhombendodekaeder" title="Rhombendodekaeder">Rhombendodekaeder</a> mit der Kantenlänge <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>b</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle b}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f11423fbb2e967f986e36804a8ae4271734917c3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}" loading="lazy"></span>.</li>
<li>Überschreitet <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>b</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle b}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f11423fbb2e967f986e36804a8ae4271734917c3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}" loading="lazy"></span> den maximalen Wert, so ist das Polyeder nicht mehr konvex und entartet schließlich für <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b=a}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>b</mi>
<mo>=</mo>
<mi>a</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle b=a}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0b2e4888d97a754d4bfa4da297b226788a73c6b8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.326ex; height:2.176ex;" alt="{\displaystyle b=a}" loading="lazy"></span> zum <a href="Sterntetraeder" title="Sterntetraeder">Sterntetraeder</a>.</li></ul>
<div class="mw-heading mw-heading2"><h2 id="Formeln">Formeln</h2></div>
<table class="toptextcells left">
<tbody><tr>
<td style="width:50%">
<div class="mw-heading mw-heading3"><h3 id="Allgemein">Allgemein</h3></div>
<p><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {a}{3}}{\sqrt {3}}<b<{\tfrac {a}{4}}{\sqrt {6}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="false" scriptlevel="0">
<mfrac>
<mi>a</mi>
<mn>3</mn>
</mfrac>
</mstyle>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>3</mn>
</msqrt>
</mrow>
<mo>&lt;</mo>
<mi>b</mi>
<mo>&lt;</mo>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="false" scriptlevel="0">
<mfrac>
<mi>a</mi>
<mn>4</mn>
</mfrac>
</mstyle>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>6</mn>
</msqrt>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\tfrac {a}{3}}{\sqrt {3}}&lt;b&lt;{\tfrac {a}{4}}{\sqrt {6}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9a08f61c1e84a156c26413301cf7abb977b17bd7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:16.803ex; height:3.509ex;" alt="{\displaystyle {\tfrac {a}{3}}{\sqrt {3}}<b<{\tfrac {a}{4}}{\sqrt {6}}}" loading="lazy"></span>
</p>
<table class="wikitable">

<tbody><tr>
<th colspan="2" style="background:#C0C0FF">Größen eines Triakisoktaeders mit Kantenlängen <i>a</i>, <i>b</i>
</th></tr>
<tr>
<td class="hintergrundfarbe5"><b><a href="Volumen" title="Volumen">Volumen</a></b>
</td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V={\frac {a^{2}}{3}}\left(a{\sqrt {2}}+2{\sqrt {3b^{2}-a^{2}}}\right)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>V</mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<msup>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mn>3</mn>
</mfrac>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>2</mn>
</msqrt>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>3</mn>
<msup>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>−<!-- − --></mo>
<msup>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</msqrt>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle V={\frac {a^{2}}{3}}\left(a{\sqrt {2}}+2{\sqrt {3b^{2}-a^{2}}}\right)}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/eace399cd82646179afd50b24335077b32a0b172.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:30.162ex; height:5.676ex;" alt="{\displaystyle V={\frac {a^{2}}{3}}\left(a{\sqrt {2}}+2{\sqrt {3b^{2}-a^{2}}}\right)}" loading="lazy"></span>
</td></tr>
<tr>
<td class="hintergrundfarbe5"><b><a href="Fl%C3%A4cheninhalt" title="Flächeninhalt">Oberflächeninhalt</a></b>
</td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{O}=6a{\sqrt {4b^{2}-a^{2}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>A</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>O</mi>
</mrow>
</msub>
<mo>=</mo>
<mn>6</mn>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>4</mn>
<msup>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>−<!-- − --></mo>
<msup>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</msqrt>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle A_{O}=6a{\sqrt {4b^{2}-a^{2}}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4a5313cbf4179be393d9d0692f96ee3a7e92efee.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.382ex; height:3.509ex;" alt="{\displaystyle A_{O}=6a{\sqrt {4b^{2}-a^{2}}}}" loading="lazy"></span>
</td></tr>
<tr>
<td class="hintergrundfarbe5"><b><a href="Pyramide_(Geometrie)#Eigenschaften" title="Pyramide (Geometrie)">Pyramidenhöhe</a></b>
</td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k={\frac {1}{3}}{\sqrt {9b^{2}-3a^{2}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>k</mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>9</mn>
<msup>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>−<!-- − --></mo>
<mn>3</mn>
<msup>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</msqrt>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle k={\frac {1}{3}}{\sqrt {9b^{2}-3a^{2}}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/804cc303313466929a83b8f201305b6cc4a016a6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:18.133ex; height:5.176ex;" alt="{\displaystyle k={\frac {1}{3}}{\sqrt {9b^{2}-3a^{2}}}}" loading="lazy"></span>
</td></tr>
<tr>
<td class="hintergrundfarbe5"><b><a href="Inkugel" title="Inkugel">Inkugelradius</a></b>
</td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho \,=a\,{\sqrt {\frac {a}{2a+4b}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>ρ<!-- ρ --></mi>
<mspace width="thinmathspace"></mspace>
<mo>=</mo>
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mfrac>
<mi>a</mi>
<mrow>
<mn>2</mn>
<mi>a</mi>
<mo>+</mo>
<mn>4</mn>
<mi>b</mi>
</mrow>
</mfrac>
</msqrt>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \rho \,=a\,{\sqrt {\frac {a}{2a+4b}}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b2133a21bd5cda94cf64e57979793c30f6797f03.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:16.857ex; height:6.176ex;" alt="{\displaystyle \rho \,=a\,{\sqrt {\frac {a}{2a+4b}}}}" loading="lazy"></span>
</td></tr>
<tr>
<td class="hintergrundfarbe5"><b>Flächenwinkel<br> &nbsp;(über Kante <i>a</i>)</b>
</td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos \,\alpha _{1}={\frac {12b^{2}-5a^{2}-8a{\sqrt {6b^{2}-2a^{2}}}}{9(4b^{2}-a^{2})}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>cos</mi>
<mspace width="thinmathspace"></mspace>
<msub>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mn>12</mn>
<msup>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>−<!-- − --></mo>
<mn>5</mn>
<msup>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>−<!-- − --></mo>
<mn>8</mn>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>6</mn>
<msup>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>−<!-- − --></mo>
<mn>2</mn>
<msup>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</msqrt>
</mrow>
</mrow>
<mrow>
<mn>9</mn>
<mo stretchy="false">(</mo>
<mn>4</mn>
<msup>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>−<!-- − --></mo>
<msup>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo stretchy="false">)</mo>
</mrow>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \cos \,\alpha _{1}={\frac {12b^{2}-5a^{2}-8a{\sqrt {6b^{2}-2a^{2}}}}{9(4b^{2}-a^{2})}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/afd701a5df99ba94446f01fff7cebcc9cbdb7be0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:38.083ex; height:7.009ex;" alt="{\displaystyle \cos \,\alpha _{1}={\frac {12b^{2}-5a^{2}-8a{\sqrt {6b^{2}-2a^{2}}}}{9(4b^{2}-a^{2})}}}" loading="lazy"></span>
</td></tr>
<tr>
<td class="hintergrundfarbe5"><b>Flächenwinkel<br> &nbsp;(über Kante <i>b</i>)</b>
</td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos \,\alpha _{2}={\frac {2b^{2}-a^{2}}{4b^{2}-a^{2}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>cos</mi>
<mspace width="thinmathspace"></mspace>
<msub>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mn>2</mn>
<msup>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>−<!-- − --></mo>
<msup>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</mrow>
<mrow>
<mn>4</mn>
<msup>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>−<!-- − --></mo>
<msup>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</mrow>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \cos \,\alpha _{2}={\frac {2b^{2}-a^{2}}{4b^{2}-a^{2}}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ddf28285194c23141b40affac41e9e3cf019eded.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:18.7ex; height:6.176ex;" alt="{\displaystyle \cos \,\alpha _{2}={\frac {2b^{2}-a^{2}}{4b^{2}-a^{2}}}}" loading="lazy"></span>
</td></tr></tbody></table>
</td>
<td>
<div class="mw-heading mw-heading3"><h3 id="Speziell">Speziell</h3></div>
<p><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b=a\,(2-{\sqrt {2}})}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>b</mi>
<mo>=</mo>
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo>−<!-- − --></mo>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>2</mn>
</msqrt>
</mrow>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle b=a\,(2-{\sqrt {2}})}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2080ba8892c67f9e42c63c33b747832c83fcd88b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.623ex; height:3.176ex;" alt="{\displaystyle b=a\,(2-{\sqrt {2}})}" loading="lazy"></span>
</p>
<table class="wikitable">

<tbody><tr>
<th colspan="2" style="background:#C0C0FF">Größen eines Triakisoktaeders mit Kantenlänge <i>a</i>
</th></tr>
<tr>
<td class="hintergrundfarbe5"><b>Volumen</b>
</td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V=a^{3}(2-{\sqrt {2}})=a^{2}b}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>V</mi>
<mo>=</mo>
<msup>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msup>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo>−<!-- − --></mo>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>2</mn>
</msqrt>
</mrow>
<mo stretchy="false">)</mo>
<mo>=</mo>
<msup>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mi>b</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle V=a^{3}(2-{\sqrt {2}})=a^{2}b}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c858cb546088912cf575f373917c09bca736a5ac.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.46ex; height:3.176ex;" alt="{\displaystyle V=a^{3}(2-{\sqrt {2}})=a^{2}b}" loading="lazy"></span>
</td></tr>
<tr>
<td class="hintergrundfarbe5"><b>Oberflächeninhalt</b>
</td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{O}=6a^{2}{\sqrt {23-16{\sqrt {2}}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>A</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>O</mi>
</mrow>
</msub>
<mo>=</mo>
<mn>6</mn>
<msup>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>23</mn>
<mo>−<!-- − --></mo>
<mn>16</mn>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>2</mn>
</msqrt>
</mrow>
</msqrt>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle A_{O}=6a^{2}{\sqrt {23-16{\sqrt {2}}}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9d2b919e97264e3337dbf237c0c46f046576a037.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:22.687ex; height:4.843ex;" alt="{\displaystyle A_{O}=6a^{2}{\sqrt {23-16{\sqrt {2}}}}}" loading="lazy"></span>
</td></tr>
<tr>
<td class="hintergrundfarbe5"><b>Inkugelradius</b>
</td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho =a{\sqrt {\frac {5+2{\sqrt {2}}}{34}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>ρ<!-- ρ --></mi>
<mo>=</mo>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mfrac>
<mrow>
<mn>5</mn>
<mo>+</mo>
<mn>2</mn>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>2</mn>
</msqrt>
</mrow>
</mrow>
<mn>34</mn>
</mfrac>
</msqrt>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \rho =a{\sqrt {\frac {5+2{\sqrt {2}}}{34}}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/71915969c1adcc588ee4f523791bd0975c6640a5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:16.954ex; height:7.676ex;" alt="{\displaystyle \rho =a{\sqrt {\frac {5+2{\sqrt {2}}}{34}}}}" loading="lazy"></span>
</td></tr>
<tr>
<td class="hintergrundfarbe5"><b><a href="Kantenkugel" title="Kantenkugel">Kantenkugelradius</a></b>
</td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r={\frac {a}{2}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>r</mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>a</mi>
<mn>2</mn>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle r={\frac {a}{2}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/808d93b47f31d9ccdac78b5494d9dbbb2dbd1259.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.213ex; height:4.676ex;" alt="{\displaystyle r={\frac {a}{2}}}" loading="lazy"></span>
</td></tr>
<tr>
<td class="hintergrundfarbe5"><b>Flächenwinkel<br>&nbsp;≈ 147° 21′</b>
</td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos \,\alpha =-{\frac {1}{17}}\,(3+8{\sqrt {2}})}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>cos</mi>
<mspace width="thinmathspace"></mspace>
<mi>α<!-- α --></mi>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>1</mn>
<mn>17</mn>
</mfrac>
</mrow>
<mspace width="thinmathspace"></mspace>
<mo stretchy="false">(</mo>
<mn>3</mn>
<mo>+</mo>
<mn>8</mn>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>2</mn>
</msqrt>
</mrow>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \cos \,\alpha =-{\frac {1}{17}}\,(3+8{\sqrt {2}})}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/d179a9671eaeb7463dc0580eaa580b9e26b90818.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:23.901ex; height:5.343ex;" alt="{\displaystyle \cos \,\alpha =-{\frac {1}{17}}\,(3+8{\sqrt {2}})}" loading="lazy"></span>
</td></tr>
<tr>
<td class="hintergrundfarbe5"><b> <a href="Sph%C3%A4rizit%C3%A4t_(Geologie)" title="Sphärizität (Geologie)">Sphärizität</a><br> &nbsp;≈ 0,92444</b>
</td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Psi ={\frac {\sqrt[{3}]{9\,\pi \left(3-2{\sqrt {2}}\right)}}{3{\sqrt {23-16{\sqrt {2}}}}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">Ψ<!-- Ψ --></mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mroot>
<mrow>
<mn>9</mn>
<mspace width="thinmathspace"></mspace>
<mi>π<!-- π --></mi>
<mrow>
<mo>(</mo>
<mrow>
<mn>3</mn>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>2</mn>
</msqrt>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</mroot>
<mrow>
<mn>3</mn>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>23</mn>
<mo>−<!-- − --></mo>
<mn>16</mn>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>2</mn>
</msqrt>
</mrow>
</msqrt>
</mrow>
</mrow>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \Psi ={\frac {\sqrt[{3}]{9\,\pi \left(3-2{\sqrt {2}}\right)}}{3{\sqrt {23-16{\sqrt {2}}}}}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/cca1c1ad4eff343f2e73cf4b9810c8df648f002a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.671ex; width:21.729ex; height:10.509ex;" alt="{\displaystyle \Psi ={\frac {\sqrt[{3}]{9\,\pi \left(3-2{\sqrt {2}}\right)}}{3{\sqrt {23-16{\sqrt {2}}}}}}}" loading="lazy"></span>
</td></tr></tbody></table>
</td></tr></tbody></table>
<div class="mw-heading mw-heading2"><h2 id="Weblinks">Weblinks</h2></div>
<div class="sisterproject" style="margin:0.1em 0 0 0;"><div class="noresize noviewer" style="display:inline-block; line-height:10px; min-width:1.6em; text-align:center;" aria-hidden="true" role="presentation"><span class="mw-default-size" typeof="mw:File"><span title="Commons"></span></span></div><b><span class=""><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Triakis_octahedron?uselang=de"><span lang="en">Commons</span>: Triakisoktaeder</a></span></b>&nbsp;– Sammlung von Bildern, Videos und Audiodateien</div>
<ul><li><a href="Eric_Weisstein" title="Eric Weisstein">Eric W. Weisstein</a>: <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/SmallTriakisOctahedron.html"><i>Triakisoktaeder</i>.</a> In: <i><a href="MathWorld" title="MathWorld">MathWorld</a></i> (englisch).</li>
<li><a href="https://www.mineralienatlas.de/lexikon/index.php/Triakisoktaeder" class="extiw external" title="mineralienatlas:Triakisoktaeder">Mineralienatlas:Triakisoktaeder</a> Interaktive Darstellung des Triakisoktaeders im <a href="Mineralienatlas" title="Mineralienatlas">Mineralienatlas</a></li></ul>
<style data-mw-deduplicate="TemplateStyles:r260755238">
/* start https://de.wikipedia.org/ */


.mw-parser-output div.klappleiste{border:1px solid var(--dewiki-rahmenfarbe1);clear:both;font-size:95%;box-sizing:border-box;margin-top:1.5em;padding:2px}.mw-parser-output div.klappleiste:after{clear:both;content:"";display:block}.mw-parser-output div.klappleiste-bild{float:left;padding:2px}.mw-parser-output div.klappleiste-kopf{background:var(--dewiki-hintergrundfarbe5);color:var(--color-base,#202122);text-align:center;font-weight:bold}.mw-parser-output div.klappleiste.mw-collapsed .klappleiste-bild{display:none}.mw-parser-output div.klappleiste+div.klappleiste,.mw-parser-output div.klappleiste+link+div.klappleiste,.mw-parser-output div.klappleiste+link+link+div.klappleiste,.mw-parser-output div.klappleiste+link+style+div.klappleiste,.mw-parser-output div.klappleiste+style+div.klappleiste,.mw-parser-output div.klappleiste+style+style+div.klappleiste,.mw-parser-output div.klappleiste+style+link+div.klappleiste{margin-top:-1px}@media screen{html.skin-theme-clientpref-night .mw-parser-output .klappleiste-bild span[typeof="mw:File"]:not(.skin-invert-image) img{background-color:#c8ccd1}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .klappleiste-bild span[typeof="mw:File"]:not(.skin-invert-image) img{background-color:#c8ccd1}}


/* end https://de.wikipedia.org/ */
</style>
<div class="klappleiste mw-collapsible navileiste navigation-not-searchable center" role="navigation">
<div class="klappleiste-kopf"><a href="Catalanischer_K%C3%B6rper" title="Catalanischer Körper">Catalanische Körper</a></div>
<div class="klappleiste-inhalt mw-collapsible-content">
<p><a href="Triakistetraeder" title="Triakistetraeder">Triakistetraeder</a>&nbsp;·
<a href="Rhombendodekaeder" title="Rhombendodekaeder">Rhombendodekaeder</a>&nbsp;·
<a href="Tetrakishexaeder" title="Tetrakishexaeder">Tetrakishexaeder</a>&nbsp;·
<a class="mw-selflink selflink">Triakisoktaeder</a>&nbsp;·
<a href="Deltoidalikositetraeder" title="Deltoidalikositetraeder">Deltoidalikositetraeder</a>&nbsp;·
<a href="Pentagonikositetraeder" title="Pentagonikositetraeder">Pentagonikositetraeder</a>&nbsp;·
<a href="Rhombentriakontaeder" title="Rhombentriakontaeder">Rhombentriakontaeder</a>&nbsp;·
<a href="Hexakisoktaeder" title="Hexakisoktaeder">Hexakisoktaeder</a>&nbsp;·
<a href="Pentakisdodekaeder" title="Pentakisdodekaeder">Pentakisdodekaeder</a>&nbsp;·
<a href="Triakisikosaeder" title="Triakisikosaeder">Triakisikosaeder</a>&nbsp;·
<a href="Deltoidalhexakontaeder" title="Deltoidalhexakontaeder">Deltoidalhexakontaeder</a>&nbsp;·
<a href="Pentagonhexakontaeder" title="Pentagonhexakontaeder">Pentagonhexakontaeder</a>&nbsp;·
<a href="Hexakisikosaeder" title="Hexakisikosaeder">Hexakisikosaeder</a>&nbsp;
</p>
</div></div></div><!--htdig_noindex--><div><div class="zim-footer">
Dieser Artikel wurde von <a class="external text" title="Zuletzt bearbeitet am 2025-06-29" href="https://de.wikipedia.org/wiki/?title=Triakisoktaeder&amp;oldid=257462808">Wikipedia</a> herausgegeben. Der Text ist unter <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.de">Creative Commons Attribution-Share Alike 4.0</a> verfügbar, sofern nicht anders angegeben. Für die Mediendateien können zusätzliche Bedingungen gelten.
</div>
</div><!--/htdig_noindex--></div>
</div>
</main>
</div>
</div>
</div>
<script src="./_webp_/webpHandler.js"></script>

</body></html>