切頂十二面体

切頂十二面体
切頂十二面体
種別	半正多面体
面数	32
面形状	正三角形: 20 正十角形: 12
辺数	90
頂点数	60
頂点形状	3, 10²（正三角形1枚と正十角形2枚が集まる）
シュレーフリ記号	t{5, 3}
ワイソフ記号	2 3 \| 5
対称群	I_h
双対多面体	三方二十面体
特性	凸集合
展開図の例
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切頂十二面体（せっちょうじゅうにめんたい、英: truncated dodecahedron）、または切頭十二面体（せっとうじゅうにめんたい）、切隅十二面体（せつぐうじゅうにめんたい）、角切り十二面体（かくぎりじゅうにめんたい）とは、半正多面体の一種で、正十二面体の各頂点を切り落としてできる立体である。

性質

一辺の長さを a とすると、

表面積: $5({\sqrt {3}}+6{\sqrt {5+2{\sqrt {5}}}})a^{2}\approx 100.99076a^{2}$
体積: ${\frac {495+235{\sqrt {5}}}{12}}a^{3}\approx 85.03966a^{3}$
外接球半径: ${\frac {\sqrt {74+30{\sqrt {5}}}}{4}}a\approx 2.969449a$
星型の数(表面のみ): 1119 (完全対称：580、捩れた星型：539)

頂点が共通となる立体

正確

不正確

小反屈変形二十・二十・十二面体

近縁な立体

正十二面体
二十・十二面体（切り込みを深くする）

二十・十二面体
（切り込みを深くする）
切頂二十面体
（切り込みを更に深くする）
側台塔切頂十二面体
（正五角台塔を追加）
切頂十二面体と三方二十面体による複合多面体

外部リンク

Weisstein, Eric W. "Truncated Dodecahedron". mathworld.wolfram.com (英語).

多面体

一様多面体

正多面体	正四面体正六面体正八面体正十二面体正二十面体
半正多面体	切頂四面体切頂六面体切頂八面体切頂十二面体切頂二十面体立方八面体二十・十二面体斜方立方八面体斜方二十・十二面体斜方切頂立方八面体斜方切頂二十・十二面体変形立方体変形十二面体
星型正多面体	小星型十二面体大十二面体大星型十二面体大二十面体
その他	八面半八面体四面半六面体小立方立方八面体大立方立方八面体立方半八面体立方切頂立方八面体一様大斜方立方八面体小斜方六面体星型切頂六面体大切頂立方八面体大斜方六面体小二重三角二十・十二面体小二十・二十・十二面体小変形二十・二十・十二面体小十二・二十・十二面体十二・十二面体切頂大十二面体斜方十二・十二面体小斜方十二面体変形十二・十二面体二重三角十二・十二面体大二重三角十二・二十・十二面体小二重三角十二・二十・十二面体二十・十二・十二面体二十面切頂十二・十二面体変形二十・十二・十二面体大二重三角二十・十二面体大二十・二十・十二面体小二十面半十二面体小十二・二十面体小十二面半十二面体大二十・十二面体切頂大二十面体斜方二十面体大変形二十・十二面体小星型切頂十二面体切頂十二・十二面体逆変形十二・十二面体大十二・二十・十二面体小十二面半二十面体大十二・二十面体大変形十二・二十・十二面体大十二面半二十面体大星型切頂十二面体一様大斜方二十・十二面体大切頂二十・十二面体大逆変形二十・十二面体大十二面半十二面体大二十面半十二面体小反屈変形二十・二十・十二面体大斜方十二面体大反屈変形二十・十二面体大二重斜方二十・十二面体

面の数による分類

その他

この項目は、多面体に関連した書きかけの項目です。この項目を加筆・訂正などしてくださる協力者を求めています。

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