查看“︁过截角正五胞体”︁的源代码

{{NoteTA|G1=Math}}
{{Infobox polychoron
| name = 过截角正五胞体
| imagename = Schlegel half-solid bitruncated 5-cell.png
| caption = [[施莱格尔投影]]
| polytope = 过截角正五胞体
| Type = [[均匀多胞体]]
| group_type = 
| Cell = 10 ([[截角四面体|''3.6.6'']]) [[Image:Truncated tetrahedron.png|20px]]
| Face = 20 {3}<br/>20 {6}
| Edge = 60
| Vertice = 30
| Vertice_type = [[Image:Bitruncated 5-cell verf.png|80px]]<BR>([[锲形体]])
| Schläfli = t<sub>1,2</sub>{3,3,3}
| Coxeter_diagram = {{CDD|node|3|node_1|3|node_1|3|node}}<BR>or {{CDD|branch_11|3ab|nodes}}
| Coxeter_group = A<sub>4</sub>, <nowiki>[[3,3,3]]</nowiki>, order 240
| Index_references = ''[[Runcinated pentachoron|5]]'' 6 ''[[Cantitruncated 5-cell|7]]''
| Symmetry_group = 
| dual = 
| Properties = [[Convex polytope|convex]], [[isogonal figure|isogonal]] [[isotoxal figure|isotoxal]], [[Isochoric figure|isochoric]]
}}
'''过截角正五胞体'''（又叫正十胞体）是一个四维多胞体, 由10个相同的三维胞[[截角四面体]]组成。每条边连接到两个[[六边形]]和一个[[三角形]]。

过截角正五胞体的五维类比是[[过截角五维正六胞体]]。它的n维类比的[[考克斯特-迪金点图]]都是中间的一个或两个点有环。

过截角正五胞体是两个由一种三维胞所组成的半正多胞体之一。另一个是[[过截角正二十四胞体]]，它由48个[[截角立方体]]组成。

== 投影 ==
{| class=wikitable
|+ [[正射投影]]
|- align=center
!A<sub>k</sub><BR>[[考克斯特平面]]
!A<sub>4</sub>
!A<sub>3</sub>
!A<sub>2</sub>
|- align=center
!Graph
|[[File:4-simplex_t12.svg|150px]]
|[[File:4-simplex_t12_A3.svg|150px]]
|[[File:4-simplex_t12_A2.svg|150px]]
|- align=center
![[二面体群]]
|[5]
|[4]
|[3]
|}

{| class=wikitable width=440
|[[File:Decachoron stereographic (hexagon).png|220px]]<BR>[[球极投影]]<br>(对着一个六边形面)
|[[File:Bitruncated 5-cell net.png|220px]]<BR>[[展开图]]
|}
== 坐标 ==

一个棱长为2的过截角正五胞体的20个顶点的[[笛卡儿坐标系]]坐标

{| 
|
:<math>\pm\left(\sqrt{\frac{5}{2}},\ \frac{5}{\sqrt{6}},\  \frac{2}{\sqrt{3}},\  0\right)</math>
:<math>\pm\left(\sqrt{\frac{5}{2}},\ \frac{5}{\sqrt{6}},\  \frac{-1}{\sqrt{3}},\ \pm1\right)</math>
:<math>\pm\left(\sqrt{\frac{5}{2}},\ \frac{1}{\sqrt{6}},\  \frac{4}{\sqrt{3}},\  0\right)</math>
:<math>\pm\left(\sqrt{\frac{5}{2}},\ \frac{1}{\sqrt{6}},\  \frac{-2}{\sqrt{3}},\ \pm2\right)</math>
:<math>\pm\left(\sqrt{\frac{5}{2}},\ -\sqrt{\frac{3}{2}},\ \pm\sqrt{3},\         \pm1\right)</math>
:<math>\pm\left(\sqrt{\frac{5}{2}},\ -\sqrt{\frac{3}{2}},\ 0,\                   \pm2\right)</math>
:<math>\pm\left(0,\                  2\sqrt{\frac{2}{3}},\ \frac{4}{\sqrt{3}},\  0\right)</math>
:<math>\pm\left(0,\                  2\sqrt{\frac{2}{3}},\ \frac{-2}{\sqrt{3}},\ \pm2\right)</math>
|}

更简单的，过截角正五胞体的顶点是五维空间[[笛卡儿坐标系]]的（0,0,1,2,2）或(1,0,0,0,-1)的全排列。

== 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]
*[[Coxeter]], ''The Beauty of Geometry: Twelve Essays'', Dover Publications, 1999, ISBN 0-486-40919-8 p.88 (Chapter 5: Regular Skew Polyhedra in three and four dimensions and their topological analogues, Proceedings of the London Mathematics Society, Ser. 2, Vol 43, 1937.) 
**Coxeter, H. S. M. ''Regular Skew Polyhedra in Three and Four Dimensions.'' Proc. London Math. Soc. 43, 33-62, 1937.
* [[Norman Johnson (mathematician)|Norman Johnson]] ''Uniform Polytopes'', Manuscript (1991)
** N.W. Johnson: ''The Theory of Uniform Polytopes and Honeycombs'', Ph.D. (1966)
*{{GlossaryForHyperspace | anchor=Pentachoron | title=Pentachoron}}
** {{PolyCell | urlname = section1.html| title = 1. Convex uniform polychora based on the pentachoron - Model 3}}
* {{KlitzingPolytopes|polychora.htm|4D|uniform polytopes (polychora)}} x3x3o3o - tip, o3x3x3o - deca

[[Category:四维几何]]
[[Category:四维多胞体]]
[[Category:多胞体]]