截角正五胞体

截角正五胞体
	施莱格尔投影; (正四面体胞在前)
类型	均匀多胞体
对偶多胞形	四角化正五胞体
识别
名称	截角正五胞体
参考索引	2 3 4
数学表示法
考克斯特符号; （英语：Coxeter-Dynkin diagram）
施莱夫利符号	t0,1{3,3,3}
性质
胞	10; 5 (3.3.3) ; 5 (3.6.6)
面	30; 20 {3}; 10 {6}
边	40
顶点	20
组成与布局
顶点图	; Irr. tetrahedron
对称性
考克斯特群	A4, [3,3,3], order 120
特性
	convex, isogonal
	查; 论; 编;

截角正五胞体由十个三维胞组成: 五个正四面体, 和五个截角四面体。每个顶点周围环绕着三个截角四面体和一个正四面体。截角正五胞体是截角四面体的四维类比。

构造

截角正五胞体的细胞可以通过在正五胞体的棱的三分点处截断其顶点。截断的五个正四面体变成新的截角四面体，并在原来的顶点处产生了五个新的正四面体。

截角四面体的六边形面彼此结合在一起，而它们的三角形面则连接到正四面体。

**正交投影**
A_k 考克斯特平面	A₄	A₃	A₂
Graph
二面体群	[5]	[4]	[3]

一个棱长为2的截角正五胞体的20个顶点的笛卡儿坐标系坐标

\left({\frac {3}{\sqrt {10}}},\ {\sqrt {3 \over 2}},\ \pm {\sqrt {3}},\ \pm 1\right)

\left({\frac {3}{\sqrt {10}}},\ {\sqrt {3 \over 2}},\ 0,\ \pm 2\right)

\left({\frac {3}{\sqrt {10}}},\ {\frac {-1}{\sqrt {6}}},\ {\frac {2}{\sqrt {3}}},\ \pm 2\right)

\left({\frac {3}{\sqrt {10}}},\ {\frac {-1}{\sqrt {6}}},\ {\frac {4}{\sqrt {3}}},\ 0\right)

\left({\frac {3}{\sqrt {10}}},\ {\frac {-5}{\sqrt {6}}},\ {\frac {1}{\sqrt {3}}},\ \pm 1\right)

\left({\frac {3}{\sqrt {10}}},\ {\frac {-5}{\sqrt {6}}},\ {\frac {-2}{\sqrt {3}}},\ 0\right)

\left(-{\sqrt {2 \over 5}},\ {\sqrt {2 \over 3}},\ {\frac {2}{\sqrt {3}}},\ \pm 2\right)

\left(-{\sqrt {2 \over 5}},\ {\sqrt {2 \over 3}},\ {\frac {-4}{\sqrt {3}}},\ 0\right)

\left(-{\sqrt {2 \over 5}},\ -{\sqrt {6}},\ 0,\ 0\right)

\left({\frac {-7}{\sqrt {10}}},\ {\frac {1}{\sqrt {6}}},\ {\frac {1}{\sqrt {3}}},\ \pm 1\right)

\left({\frac {-7}{\sqrt {10}}},\ {\frac {1}{\sqrt {6}}},\ {\frac {-2}{\sqrt {3}}},\ 0\right)

\left({\frac {-7}{\sqrt {10}}},\ -{\sqrt {3 \over 2}},\ 0,\ 0\right)

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

截角正五胞体
施莱格尔投影 (正四面体胞在前)
类型	均匀多胞体
对偶多胞形	四角化正五胞体
识别
名称	截角正五胞体
参考索引	2 3 4
数学表示法
考克斯特符号（英语：Coxeter-Dynkin diagram）
施莱夫利符号	t_0,1{3,3,3}
性质
胞	10 5 *(3.3.3)* 5 (3.6.6)
面	30 20 {3} 10 {6}
边	40
顶点	20
组成与布局
顶点图	Irr. tetrahedron
对称性
考克斯特群	A₄, [3,3,3], order 120
特性
convex, isogonal
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