截半超立方體

{{Infobox polychoron
| name = 截半超立方体
| imagename = Schlegel half-solid rectified 8-cell.png
| caption = 施莱格尔投影(显示16个正四面体胞)
| polytope = 截半超立方体
| Type = 均匀多胞体
| group_type =
| Cell =24
16 (3.3.3) 8 (3.4.3.4)
| Face =88
64 {3}24 {4}
| Edge =96
| Vertice =32
| Vertice_type =(細長等邊三角形棱鏡)
| Schläfli =t1{4,3,3}
| Symmetry_group =
| dual =
| Properties =convex, isogonal, isotoxal
| Index_references = 1 2 3
| Coxeter_group =B4, [4,3,3], order 384
| Coxeter_diagram =
}}
: 三角柱5个面:

2(3.3.3)和3(3.4.3.4)
]]

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。

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。

结合
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。

投影
坐标
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)

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。

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 [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html]
** (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]

• Uniform Polytopes, Manuscript (1991)

* N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs*, Ph.D. (1966)
*
*

外部链接

• [http://www.polytope.de/nr03.html Rectified 5-cell] - data and images

**
*