截角正二十四胞体由48个三维胞组成: 24个立方体, 和24个截角八面体。每个顶点周围环绕着三个截角八面体和一个立方体。[1] Quick Facts 截角正二十四胞体, 类型 ...截角正二十四胞体施莱格尔投影(立方体胞在前)类型均匀多胞体识别名称截角正二十四胞体参考索引2 3 4数学表示法考克斯特符号(英语:Coxeter-Dynkin diagram)施莱夫利符号t0,1{3,4,3}性质胞1024 (4.4.4) 24 (4.6.6) 面240144 {4}96 {6}边384顶点144组成与布局顶点图Irr. tetrahedron对称性考克斯特群F4, [3,4,3], order 1152特性convex, isogonal,环带多胞体查论编Close 截角正二十四胞体的细胞可以通过在正二十四胞体的棱的三分点处截断其顶点。截断的24个正八面体变成新的截角八面体,并在原来的顶点处产生了24个新的立方体。 截角八面体的六边形面彼此结合在一起,而它们的正方形面则连接到立方体。 More information Fk 考克斯特平面, F4 ... 正交投影 Fk考克斯特平面 F4 B4 B3 B2 Graph 二面体群 [12] [6] [8] [4] Close 展开图 球极投影(对着一个 截角八面体胞) 一个棱长为2的截角正二十四胞体的144个顶点的笛卡儿坐标系坐标 ( 3 10 , 3 2 , ± 3 , ± 1 ) {\displaystyle \left({\frac {3}{\sqrt {10}}},\ {\sqrt {3 \over 2}},\ \pm {\sqrt {3}},\ \pm 1\right)} ( 3 10 , 3 2 , 0 , ± 2 ) {\displaystyle \left({\frac {3}{\sqrt {10}}},\ {\sqrt {3 \over 2}},\ 0,\ \pm 2\right)} ( 3 10 , − 1 6 , 2 3 , ± 2 ) {\displaystyle \left({\frac {3}{\sqrt {10}}},\ {\frac {-1}{\sqrt {6}}},\ {\frac {2}{\sqrt {3}}},\ \pm 2\right)} ( 3 10 , − 1 6 , 4 3 , 0 ) {\displaystyle \left({\frac {3}{\sqrt {10}}},\ {\frac {-1}{\sqrt {6}}},\ {\frac {4}{\sqrt {3}}},\ 0\right)} ( 3 10 , − 5 6 , 1 3 , ± 1 ) {\displaystyle \left({\frac {3}{\sqrt {10}}},\ {\frac {-5}{\sqrt {6}}},\ {\frac {1}{\sqrt {3}}},\ \pm 1\right)} ( 3 10 , − 5 6 , − 2 3 , 0 ) {\displaystyle \left({\frac {3}{\sqrt {10}}},\ {\frac {-5}{\sqrt {6}}},\ {\frac {-2}{\sqrt {3}}},\ 0\right)} ( − 2 5 , 2 3 , 2 3 , ± 2 ) {\displaystyle \left(-{\sqrt {2 \over 5}},\ {\sqrt {2 \over 3}},\ {\frac {2}{\sqrt {3}}},\ \pm 2\right)} ( − 2 5 , 2 3 , − 4 3 , 0 ) {\displaystyle \left(-{\sqrt {2 \over 5}},\ {\sqrt {2 \over 3}},\ {\frac {-4}{\sqrt {3}}},\ 0\right)} ( − 2 5 , − 6 , 0 , 0 ) {\displaystyle \left(-{\sqrt {2 \over 5}},\ -{\sqrt {6}},\ 0,\ 0\right)} ( − 7 10 , 1 6 , 1 3 , ± 1 ) {\displaystyle \left({\frac {-7}{\sqrt {10}}},\ {\frac {1}{\sqrt {6}}},\ {\frac {1}{\sqrt {3}}},\ \pm 1\right)} ( − 7 10 , 1 6 , − 2 3 , 0 ) {\displaystyle \left({\frac {-7}{\sqrt {10}}},\ {\frac {1}{\sqrt {6}}},\ {\frac {-2}{\sqrt {3}}},\ 0\right)} ( − 7 10 , − 3 2 , 0 , 0 ) {\displaystyle \left({\frac {-7}{\sqrt {10}}},\ -{\sqrt {3 \over 2}},\ 0,\ 0\right)} 更简单的,截角正二十四胞体的顶点是五维空间笛卡儿坐标系的(0,0,0,1,2)或(0,1,2,2,2)的全排列。 [1]截角正二十四胞体是截角八面体的四维类比。 H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, editied by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1] (页面存档备份,存于互联网档案馆) (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591] (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999, ISBN 0-486-40919-8 p.88 (Chapter 5: Regular Skew Polyhedra in three and four dimensions and their topological analogues, Proceedings of the London Mathematics Society, Ser. 2, Vol 43, 1937.) Coxeter, H. S. M. Regular Skew Polyhedra in Three and Four Dimensions. Proc. London Math. Soc. 43, 33-62, 1937. Norman Johnson Uniform Polytopes, Manuscript (1991) N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966) Olshevsky, George, Pentachoron at Glossary for Hyperspace. 1. Convex uniform polychora based on the pentachoron - Model 3, George Olshevsky. Klitzing, Richard. 4D uniform polytopes (polychora). bendwavy.org. x3x3o3o - tip, o3x3x3o - decaWikiwand in your browser!Seamless Wikipedia browsing. On steroids.Every time you click a link to Wikipedia, Wiktionary or Wikiquote in your browser's search results, it will show the modern Wikiwand interface.Wikiwand extension is a five stars, simple, with minimum permission required to keep your browsing private, safe and transparent.Wikiwand for ChromeWikiwand for Firefox
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