过截角正五胞体

过截角正五胞体（又叫正十胞体）是一个四维多胞体, 由10个相同的三维胞截角四面体组成。每条边连接到两个六边形和一个三角形。

过截角正五胞体的五维类比是过截角五维正六胞体。它的n维类比的考克斯特-迪金点图都是中间的一个或两个点有环。

过截角正五胞体是两个由一种三维胞所组成的半正多胞体之一。另一个是过截角正二十四胞体，它由48个截角立方体组成。

 投影 
+ 正射投影Ak考克斯特平面A4A3A2Graph150px150px150px二面体群[5][4][3]

220px球极投影(对着一个六边形面)220px展开图
 坐标 

一个棱长为2的过截角正五胞体的20个顶点的笛卡儿坐标系坐标

更简单的，过截角正五胞体的顶点是五维空间笛卡儿坐标系的（0,0,1,2,2）或(1,0,0,0,-1)的全排列。

 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