过截角正五胞体
外观
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过截角正五胞体 | |
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类型 | 均匀多胞体 |
识别 | |
名称 | 过截角正五胞体 |
参考索引 | 5 6 7 |
数学表示法 | |
考克斯特符号 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() or ![]() ![]() ![]() |
施莱夫利符号 | t1,2{3,3,3} |
性质 | |
胞 | 10 (3.6.6) ![]() |
面 | 20 {3} 20 {6} |
边 | 60 |
顶点 | 30 |
组成与布局 | |
顶点图 | ![]() (锲形体) |
对称性 | |
考克斯特群 | A4, [[3,3,3]], order 240 |
特性 | |
convex, isogonal isotoxal, isochoric | |
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
[编辑]Ak 考克斯特平面 |
A4 | A3 | A2 |
---|---|---|---|
Graph | ![]() |
![]() |
![]() |
二面体群 | [5] | [4] | [3] |
![]() 球极投影 (对着一个六边形面) |
![]() 展开图 |
坐标
[编辑]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
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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
[编辑]- 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 - deca