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。
更多信息 Ak 考克斯特平面, A4 ...
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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
![{\displaystyle \pm \left({\sqrt {\frac {5}{2}}},\ {\frac {5}{\sqrt {6}}},\ {\frac {2}{\sqrt {3}}},\ 0\right)}](//wikimedia.org/api/rest_v1/media/math/render/svg/13a187180a1eb8de70cfc982160e1fc4499125f2)
![{\displaystyle \pm \left({\sqrt {\frac {5}{2}}},\ {\frac {5}{\sqrt {6}}},\ {\frac {-1}{\sqrt {3}}},\ \pm 1\right)}](//wikimedia.org/api/rest_v1/media/math/render/svg/fc240cf067f7ec30f77a7f0bb04db0008857d99c)
![{\displaystyle \pm \left({\sqrt {\frac {5}{2}}},\ {\frac {1}{\sqrt {6}}},\ {\frac {4}{\sqrt {3}}},\ 0\right)}](//wikimedia.org/api/rest_v1/media/math/render/svg/8742d4aa8080618a6e8364dc0c16aa6962c95c44)
![{\displaystyle \pm \left({\sqrt {\frac {5}{2}}},\ {\frac {1}{\sqrt {6}}},\ {\frac {-2}{\sqrt {3}}},\ \pm 2\right)}](//wikimedia.org/api/rest_v1/media/math/render/svg/e9d23e44ca880938ae64684b4c625ce031a99d37)
![{\displaystyle \pm \left({\sqrt {\frac {5}{2}}},\ -{\sqrt {\frac {3}{2}}},\ \pm {\sqrt {3}},\ \pm 1\right)}](//wikimedia.org/api/rest_v1/media/math/render/svg/305d2cd193d1411c3748613b126d7c9b05289b3c)
![{\displaystyle \pm \left({\sqrt {\frac {5}{2}}},\ -{\sqrt {\frac {3}{2}}},\ 0,\ \pm 2\right)}](//wikimedia.org/api/rest_v1/media/math/render/svg/9e57827f91cace6552ff0be6f3da311c852ab3d5)
![{\displaystyle \pm \left(0,\ 2{\sqrt {\frac {2}{3}}},\ {\frac {4}{\sqrt {3}}},\ 0\right)}](//wikimedia.org/api/rest_v1/media/math/render/svg/c75f92cda6070ad8cb3a9f2047bcdd900444b1eb)
![{\displaystyle \pm \left(0,\ 2{\sqrt {\frac {2}{3}}},\ {\frac {-2}{\sqrt {3}}},\ \pm 2\right)}](//wikimedia.org/api/rest_v1/media/math/render/svg/5306d69f20d26f5ba5ad5ea64071772e11a5512c)
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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。
- 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