查看“截角超立方體”的源代码

{{Polytopebox
| name = 截角超立方体
| imagename = Schlegel half-solid truncated tesseract.png
| caption = [[施莱格尔投影]]<BR>(可以看见[[正四面体]]胞)
| polytope = 截角超立方体
| Type = [[均匀多胞体]]
| group_type = 
| Cell = 24<br/>8 [[截角立方体|''3.8.8'']] [[Image:Truncated hexahedron.png|20px]]<BR>16 [[正四面体|''3.3.3'']] [[Image:Tetrahedron.png|20px]]
| Face = 88<br/>64 [[三角形|{3}]]<BR>24 [[八边形|{8}]]
| Edge =128
| Vertice =64
| Vertice_type =[[Image:Truncated 8-cell verf.png|80px]]<BR>Isosceles triangular pyramid
| Schläfli =t<sub>0,1</sub>{4,3,3}
| Symmetry_group = 
| dual = 
| Properties =[[Convex polytope|convex]]
| Index_references = ''[[正十六胞体|12]]'' 13 ''[[Cantellated tesseract|14]]''
| Coxeter_group =BC<sub>4</sub>, [4,3,3], order 384
| Coxeter_diagram = {{CDD|node_1|4|node_1|3|node|3|node}}
}}
'''截角超立方体'''有24个[[胞]]:8个[[截角立方体]]，和16个[[正四面体]]。

==坐标==

截角超立方体可以通过在每条棱距离顶点<math>1/(\sqrt{2}+2)</math>处截断[[超立方体]]的每一个角来得到。每个截断的角会产生一个[[正四面体]]。

一个棱长为2的截角超立方体的每个顶点的[[笛卡儿坐标系]]坐标为:

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

== 投影 ==
{| class=wikitable
|+ [[正交投影]]
|- align=center
![[考克斯特平面]]
!B<sub>4</sub>
!B<sub>3</sub> / D<sub>4</sub> / A<sub>2</sub>
!B<sub>2</sub> / D<sub>3</sub>
|- align=center
!Graph
|[[File:4-cube_t01.svg|160px]]
|[[File:4-cube t01 B3.svg|160px]]
|[[File:4-cube t01 B2.svg|160px]]
|- align=center
![[二面体群]]
|[8]
|[6]
|[4]
|- align=center
![[考克斯特平面]]
!F<sub>4</sub>
!A<sub>3</sub>
|- align=center
!Graph
|[[File:4-cube t01 F4.svg|160px]]
|[[File:4-cube t01 A3.svg|160px]]
|- align=center
![[二面体群]]
|[12/3]
|[4]
|}

{| class="wikitable"
|[[Image:Truncated tesseract net.png|200px]]<BR>[[展开图]]
|[[Image:Truncated tesseract stereographic (tC).png|200px]]<BR>三维正交投影
|}

== 参考文献 ==
* [[Thorold Gosset|T. Gosset]]: ''On the Regular and Semi-Regular Figures in Space of n Dimensions'', Messenger of Mathematics, Macmillan, 1900
* [[Harold Scott MacDonald Coxeter|H.S.M. Coxeter]]:
** Coxeter, ''[[Regular Polytopes (book)|Regular Polytopes]]'', (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8, p.&nbsp;296, Table I (iii): Regular Polytopes, three regular polytopes in n-dimensions (n≥5)
** H.S.M. Coxeter, ''Regular Polytopes'', 3rd Edition, Dover New York, 1973, p.&nbsp;296, Table I (iii): Regular Polytopes, three regular polytopes in n-dimensions (n≥5)
** '''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]
* [[John Horton Conway|John H. Conway]], Heidi Burgiel, Chaim Goodman-Strass, ''The Symmetries of Things'' 2008, ISBN 978-1-56881-220-5 (Chapter 26. pp.&nbsp;409: Hemicubes: 1<sub>n1</sub>)
* [[Norman Johnson (mathematician)|Norman Johnson]] ''Uniform Polytopes'', Manuscript (1991)
** N.W. Johnson: ''The Theory of Uniform Polytopes and Honeycombs'', Ph.D. (1966)
* {{PolyCell | urlname = section2.html| title = 2. Convex uniform polychora based on the tesseract (8-cell) and hexadecachoron (16-cell) - Models 13, 16, 17}}
* {{KlitzingPolytopes|polychora.htm|4D|uniform polytopes (polychora)}} o3o3o4o  - tat, o3x3x4o - tah, x3x3o4o - thex
<references/>

== 外部链接 ==
* [http://www.software3d.com/Tat.php Paper model of truncated tesseract] created using nets generated by [[Stella (software)|Stella4D]] software

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