# 正二十四胞体堆砌

{3,4}
{3}

r{3,3,4,3}
2r{4,3,3,4}
2r{4,3,31,1}
{31,1,1,1}

${\displaystyle {\tilde {C}}_{4}}$, [4,3,3,4]
${\displaystyle {\tilde {B}}_{4}}$, [4,3,31,1]
${\displaystyle {\tilde {D}}_{4}}$, [31,1,1,1]

## 性质

### 牛顿数

${\displaystyle {\frac {\pi ^{2}}{16}}\cong 0.61685}$

### 顶点座标

${\displaystyle \left\{(x_{i})\in \mathbb {Z} ^{4}:{\textstyle \sum _{i}}x_{i}\equiv 0\;({\mbox{mod }}2)\right\}}$

## 相关多胞体与堆砌

 图像 施莱夫利符号 超立方体堆砌 正十六胞体堆砌 正二十四胞体堆砌 {4,3,3,4} {3,3,4,3} {3,4,3,3}

• 截角正五胞体堆砌
• 全截正五胞体堆砌
• 截角正二十四胞体堆砌
• 截半正二十四胞体堆砌
• 扭棱正二十四胞体堆砌

## 参考文献

1. ^ Richard Klitzing, 4D, Euclidean tesselations o4o3x3o4o, o3x3o *b3o4o, o3x3o *b3o4o, o3x3o4o3o, o3o3o4o3x - icot - O88
2. ^ O. R. Musin. The problem of the twenty-five spheres. Russ. Math. Surv. 2003, 58: 794–795. doi:10.1070/RM2003v058n04ABEH000651.
• Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8 p. 296, Table II: Regular honeycombs
• Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]页面存档备份，存于互联网档案馆
• (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
• George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs) - Model 88