截角超立方體

{{Infobox polychoron
| name = 截角超立方体
| imagename = Schlegel half-solid truncated tesseract.png
| caption = 施莱格尔投影(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
8 3.8.8 16 3.3.3
| Face = 88
64 {3}24 {8}
| Edge =128
| Vertice =64
| Vertice_type =Isosceles triangular pyramid
| Schläfli =t0,1{4,3,3}
| Symmetry_group =
| dual =
| Properties =convex
| Index_references = 12 13 14
| Coxeter_group =BC4, [4,3,3], order 384
| Coxeter_diagram =
}}
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1/(\sqrt{2}+2)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:

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

投影
参考文献

• 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*, (3rd edition, 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*, 3rd Edition, 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**, 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 H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 26. pp. 409: Hemicubes: 1n1)
• Norman Johnson Uniform Polytopes, Manuscript (1991)

* N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs*, Ph.D. (1966)
*

• o3o3o4o - tat, o3x3x4o - tah, x3x3o4o - thex

外部链接

• [https://www.software3d.com/Tat.php Paper model of truncated tesseract] created using nets generated by Stella4D software