查看“︁截角五维超正方体”︁的源代码

{{NoteTA|G1=Math}}
{{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 =[[File:Truncated 5-cube verf.png|40px]]<BR>Elongated tetrahedral pyramid
| Schläfli =t{4,3,3,3}
| Symmetry_group = 
| dual = 
| Properties =[[Convex polytope|convex]]
| Index_references = 
| Coxeter_group =BC<sub>5</sub>, [3,3,3,4]
| Coxeter_diagram = {{CDD|node_1|4|node_1|3|node|3|node|3|node}}
}}

''截角五维超正方体''可以通过在每条棱距离顶点<math>1/(\sqrt{2}+2)</math>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:

:<math>\left(\pm1,\ \pm(1+\sqrt{2}),\ \pm(1+\sqrt{2}),\ \pm(1+\sqrt{2}),\ \pm(1+\sqrt{2})\right)</math>

== 投影 ==

{| class=wikitable
|+ [[正交投影]]
|- align=center
![[考克斯特平面]]
!B<sub>5</sub>
!B<sub>4</sub> / D<sub>5</sub>
!B<sub>3</sub> / D<sub>4</sub> / A<sub>2</sub>
|- align=center
!Graph
|[[File:5-cube t01.svg|150px]]
|[[File:5-cube t01_B4.svg|150px]]
|[[File:5-cube t01_B3.svg|150px]]
|- align=center
![[二面体群]]
|[10]
|[8]
|[6]
|- align=center
![[考克斯特平面]]
!B<sub>2</sub>
!A<sub>3</sub>
|- align=center
!Graph
|[[File:5-cube t01_B2.svg|150px]]
|[[File:5-cube t01_A3.svg|150px]]
|- align=center
![[二面体群]]
|[4]
|[4]
|}

''截角五维超正方体''是各维度截角[[超方形]]中的第四个:
{| class=wikitable
|+ 截角超方形
|- align=center
|[[File:Regular polygon 8 annotated.svg|60px]]
|[[File:3-cube_t01.svg|60px]][[File:Truncated hexahedron.png|60px]]
|[[File:4-cube_t01.svg|60px]][[File:Schlegel half-solid truncated tesseract.png|60px]]
|[[File:5-cube_t01.svg|60px]][[File:5-cube_t01 A3.svg|60px]]
|[[File:6-cube_t01.svg|60px]][[File:6-cube_t01 A5.svg|60px]]
|[[File:7-cube_t01.svg|60px]][[File:7-cube_t01 A5.svg|60px]]
|[[File:8-cube_t01.svg|60px]][[File:8-cube_t01 A7.svg|60px]]
|rowspan=3|...
|- align=center
|[[八边形]]
|[[截角立方体]]
|[[截角正八胞体]]
|截角五维超正方体
|[[截角六维超正方体]]
|[[截角七维超正方体]]
|[[截角八维超正方体]]
|- align=center
|{{CDD|node_1|4|node_1}}
|{{CDD|node_1|4|node_1|3|node}}
|{{CDD|node_1|4|node_1|3|node|3|node}}
|{{CDD|node_1|4|node_1|3|node|3|node|3|node}}
|{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node}}
|{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node|3|node}}
|{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node|3|node|3|node}}
|}

== 参考文献 ==
* [[Harold Scott MacDonald Coxeter|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] {{Wayback|url=http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html |date=20160711140441 }}
*** (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 (mathematician)|Norman Johnson]] ''Uniform Polytopes'', Manuscript (1991)
** N.W. Johnson: ''The Theory of Uniform Polytopes and Honeycombs'', Ph.D. 
* {{KlitzingPolytopes|polytera.htm|5D|uniform polytopes (polytera)}} o3o3o3x4x - tan, o3o3x3x4o - bittin

== 外部链接 ==
* {{MathWorld|title=Hypercube|urlname=Hypercube}}
*{{GlossaryForHyperspace | anchor=Measure | title=Measure polytope }}
* [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] {{Wayback|url=http://tetraspace.alkaline.org/glossary.htm |date=20091022011912 }}

[[Category:多胞体]]