截半正五胞体

{{Infobox polychoron
| name = 截半正五胞体
| imagename = Schlegel half-solid rectified 5-cell.png
| caption = 施莱格尔投影（显示5个正四面体胞）
| polytope = 截半正五胞体
| Type = 均匀多胞体
| group_type =
| Cell =10
5 (3.3.3) 5 (3.3.3.3)
| Face =30 {3}
| Edge =30
| Vertice =10
| Vertice_type =三角柱
| Schläfli =t1{3,3,3}
| Symmetry_group =
| dual =
| Properties =convex, isogonal, isotoxal
| Index_references = 1 2 3
| Coxeter_group =A4, [3,3,3], order 120
| Coxeter_diagram =
}}
: 三角柱5个面:

2(3.3.3)和3(3.3.3.3)
]]
在四维几何学中,截半正五胞体是一个由5个正四面体和5个正八面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正八面体。每个顶点周围环绕着两个正四面体和三个正八面体。它总共有30个三角形面，30条棱和10个顶点。它的顶点图是正三角柱。截半正五胞体是三个由两种或更多的正多面体胞组成的四维半正多胞体之一。

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2的截半正五胞体的顶点的笛卡儿坐标系坐标

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

• T. Gosset: On the Regular and Semi-Regular Figures in Space of n Dimensions, Messenger of Mathematics, Macmillan, 1900
• 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]

• Norman Johnson 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

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