截角正二十四胞体

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。截角正二十四胞体是截角八面体的四维类比。

构造

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。

结合

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。

 投影 
+ 正交投影Fk考克斯特平面F4B4B3B2Graph150px150px150px二面体群[12][6][8][4]

坐标

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

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。

 注释 

 参考文献 
 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  
 (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)


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Category:四维几何
Category:四维多胞体
Category:多胞体