过截角正二十四胞体

过截角正二十四胞体(又叫正四十八胞体)是一个四维多胞体, 由48个相同的三维胞截角立方体组成。每条边连接到两个八边形和一个三角形

过截角正二十四胞体
类型均匀多胞体
识别
名称过截角正二十四胞体
参考索引5 6 7
数学表示法
考克斯特符号
英语Coxeter-Dynkin diagram
node 3 node_1 4 node_1 3 node 
or branch_11 3ab nodes 
施莱夫利符号t1,2{3,4,3}
性质
48 (3.8.8)
336
192 {3}
144 {8}
576
顶点288
组成与布局
顶点图
(锲形体)
对称性
考克斯特群F4, [[3,4,3]], order 2304
特性
convex, isogonal isotoxal, isochoric

过截角正二十四胞体是两个由一种三维胞所组成的半正多胞体之一。另一个是过截角正五胞体,它由10个截角四面体组成。

投影

正射投影
Ak
考克斯特平面
A4 A3 A2
Graph      
二面体群 [5] [4] [3]
 
球极投影
(对着一个八边形面)

展开图

坐标

一个棱长为2的过截角正二十四胞体的288个顶点的笛卡儿坐标系坐标

 
 
 
 
 
 
 
 

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 [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.
  • Klitzing, Richard. 4D uniform polytopes (polychora). bendwavy.org.  x3x3o3o - tip, o3x3x3o - deca