截半超立方體

截半超立方体()，在四维几何学中，是一个由16个正四面体和8个截半立方体胞组成的均匀多胞体。每条棱都连接到一个正四面体和两个截半立方体。每个顶点周围环绕着两个正四面体和三个截半立方体。它总共有88个面（64个三角形面和24个正方形面），96条棱和32个顶点。它的顶点图是正三角柱。

顶点图: 三角柱
5个面:

2(3.3.3)和3(3.4.3.4)

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	[8]	[6]	[4]

施莱格尔投影 (对着一个截半立方体胞)	展开图
	截半立方体为中心的3维透视投影，最接近的截半立方体呈红色，周围的4个截半立方体呈绿色。远端的胞清晰度降低(虽然可以从棱看出它们)。投影只是在三维空间中旋转，而不是在四维空间中旋转。

一个棱长为 ${\sqrt {2}}$ 的截半超立方体的顶点的笛卡儿坐标系坐标

\left(0,\ 0,\ 0,\ 0\right)

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

\left({\sqrt {\frac {2}{5}}},\ {\frac {2}{\sqrt {6}}},\ {\frac {-1}{\sqrt {3}}},\ \pm 1\right)

\left({\sqrt {\frac {2}{5}}},\ {\frac {-2}{\sqrt {6}}},\ {\frac {1}{\sqrt {3}}},\ \pm 1\right)

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

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

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

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

更简单的，截半正五胞体的顶点是五维空间笛卡儿坐标系的(0,0,0,1,1)或(0,0,1,1,1)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
  - (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]
Norman Johnson Uniform Polytopes, Manuscript (1991)
- N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966)
2. Convex uniform polychora based on the tesseract (8-cell) and hexadecachoron (16-cell) - Model 11, George Olshevsky.
Richard Klitzing, 4D uniform polytopes (polychora), o4x3o3o - rit

Rectified 5-cell - data and images
- 1. Convex uniform polychora based on the pentachoron - Model 2, George Olshevsky.
Richard Klitzing, 4D uniform polytopes (polychora), x3o3o3o - rap

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