过截角正二十四胞体

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Template:NoteTA Template:Infobox polychoron 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

±(52, 56, 23, 0)
±(52, 56, −13, ±1)
±(52, 16, 43, 0)
±(52, 16, −23, ±2)
±(52, −32, ±3, ±1)
±(52, −32, 0, ±2)
±(0, 223, 43, 0)
±(0, 223, −23, ±2)

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] Template:Wayback
      • (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)
  • Template:GlossaryForHyperspace
  • Template:KlitzingPolytopes x3x3o3o - tip, o3x3x3o - deca
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