截角五维超正方体

{{Infobox polytope
| name = 截角五维超正方体
| imagename = 5-cube t01.svg
| caption =
| polytope = 截角五维超正方体
| Type = 五维均匀多胞体
| Dimension = 5
| dim1 = 四维
| count1 = 42
| group_type =
| Cell =200
| Face =400
| Edge =400
| Vertice =160
| Vertice_type =Elongated tetrahedral pyramid
| Schläfli =t{4,3,3,3}
| Symmetry_group =
| dual =
| Properties =convex
| Index_references =
| Coxeter_group =BC5, [3,3,3,4]
| Coxeter_diagram =
}}

截角五维超正方体可以通过在每条棱距离顶点1/(\sqrt{2}+2)处截断五维超正方体的顶点来得到。每个被截断的顶点会产生一个新的正五胞体。

坐标
一个棱长为2的截角五维超正方体的每个顶点的笛卡儿坐标系坐标为:

:\left(\pm1,\ \pm(1+\sqrt{2}),\ \pm(1+\sqrt{2}),\ \pm(1+\sqrt{2}),\ \pm(1+\sqrt{2})\right)

投影
截角五维超正方体是各维度截角超方形中的第四个:

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]

• Norman Johnson Uniform Polytopes, Manuscript (1991)

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

• o3o3o3x4x - tan, o3o3x3x4o - bittin

外部链接
*
*

• [https://web.archive.org/web/20070310205351/http://members.cox.net/hedrondude/topes.htm Polytopes of Various Dimensions]
• [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]