大星型切頂十二面体

大星型切頂十二面体 (だいほしがたせっちょうじゅうにめんたい、Great Stellated Truncated Dodecahedron)又は擬切頂大星型十二面体 (ぎせっちょうだいほしがたじゅうにめんたい、Quasitruncated Great Stellated Dodecahedron)とは、一様多面体の一種で、大星型十二面体の星型五角形が星型十角形になるようにして各頂点を削ったものである。切り口は正三角形であるが、外観上は3枚の凧形となる。また、切頂十二面体の正十角形を、正10/3角形に変更した図形でもある。詳しくは星型切頂六面体を参照。

性質

構成面：正三角形 20枚、星型十角形 12枚
辺： 90
頂点： 60
頂点形状： 3, 10/3, 10/3
シュレーフリ記号: t{5/3,3}
ワイソフ記号： 2 3 | 5/3
枠：正方形が黄金長方形になっている斜方二十・十二面体
双対：大三方二十面体（英語版）
外接球半径：一辺を2とすると ${\sqrt {37-15{\sqrt {5}} \over 2}}$

同じ枠を持つ立体

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

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