# 正十六胞体

（16-胞）
4-体

16 (3.3.3)
32 {3}
24

(3.3.3.3)

## 几何

(±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1)。

### 对称群构造

{3,31,1}
[31,1,1] = [1+,4,3,3] 192
4-4 复棱锥英语duopyramid {4}+{4} [[4,2,4]] 128

4-长菱体英语rhombic fusil
{3,3,4} [3,3,4] 384
{4}+{4} [[4,2,4]] 128
{3,4}+{} [4,3,2] 96
{4}+{}+{} [4,2,2] 32
{}+{}+{}+{} [2,2,2] 16

## 可视化

 在4阶皮特里多边形（英语：Petrie polygon）对称性中的截半超正方体，也作为交错超正方体 四维超正方体

## 参考

• T. Gosset: On the Regular and Semi-Regular Figures in Space of n Dimensions, Messenger of Mathematics, Macmillan, 1900
• H.S.M. Coxeter:
• Coxeter, Regular Polytopes, (第三版, 1973), Dover edition, ISBN 0-486-61480-8, p.296, Table I (iii): Regular Polytopes, three regular polytopes in n-dimensions (n≥5)
• H.S.M. Coxeter, Regular Polytopes, 第三版, Dover New York, 1973, p.296, Table I (iii): Regular Polytopes, three regular polytopes in n-dimensions (n≥5)
• Kaleidoscopes: Selected Writings of H.S.M. Coxeter,F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication参与修改, 1995, ISBN 978-0-471-01003-6 [1]
• (22页) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
• (23页) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
• (24页) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
• John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (26章.409页: Hemicubes: 1n1)
• Norman Johnson Uniform Polytopes, Manuscript (1991)
• N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966)
• Regular Convex Four-Dimensional Polytopes 提供了正十六胞体的部分几何数据。

{3,3,3} {4,3,3} {3,3,4} {3,4,3} {5,3,3} {3,3,5}