# 截半正五胞体

10
5 (3.3.3)
5 (3.3.3.3) 20px
30 {3}
30

5个面:

2(3.3.3)和3(3.3.3.3)

## 投影

Ak

A4 A3 A2
Graph

 施莱格尔投影 (对着一个正八面体胞) 展开图 正四面体为中心的3维透视投影，最接近的正四面体呈红色，周围的4个正八面体呈绿色。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。

## 坐标

 $\left(\sqrt{\frac{2}{5}},\ \frac{2}{\sqrt{6}},\ \frac{2}{\sqrt{3}},\ 0 \right)$ $\left(\sqrt{\frac{2}{5}},\ \frac{2}{\sqrt{6}},\ \frac{-1}{\sqrt{3}},\ \pm1\right)$ $\left(\sqrt{\frac{2}{5}},\ \frac{-2}{\sqrt{6}},\ \frac{1}{\sqrt{3}},\ \pm1\right)$ $\left(\sqrt{\frac{2}{5}},\ \frac{-2}{\sqrt{6}},\ \frac{-2}{\sqrt{3}},\ 0 \right)$ $\left(\frac{-3}{\sqrt{10}},\ \frac{1}{\sqrt{6}},\ \frac{1}{\sqrt{3}},\ \pm1\right)$ $\left(\frac{-3}{\sqrt{10}},\ \frac{1}{\sqrt{6}},\ \frac{-2}{\sqrt{3}},\ 0 \right)$ $\left(\frac{-3}{\sqrt{10}},\ -\sqrt{\frac{3}{2}},\ 0,\ 0 \right)$

## 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 [1]
• (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)