截角超立方体

截角超立方体
截角超立方体
	施莱格尔投影; (可以看见正四面体胞)
类型	均匀多胞体
识别
名称	截角超立方体
参考索引	12 13 14
数学表示法
考克斯特符号; （英语：Coxeter-Dynkin diagram）
施莱夫利符号	t0,1{4,3,3}
性质
胞	24; 8 3.8.8 ; 16 3.3.3
面	88; 64 {3}; 24 {8}
边	128
顶点	64
组成与布局
顶点图	; Isosceles triangular pyramid
对称性
考克斯特群	BC4, [4,3,3], order 384
特性
	convex
	查; 论; 编;

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

投影

正交投影
考克斯特平面	B₄	B₃ / D₄ / A₂	B₂ / D₃
Graph
二面体群	[8]	[6]	[4]
考克斯特平面	F₄	A₃
Graph
二面体群	[12/3]	[4]

展开图	三维正交投影

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 [1] （页面存档备份，存于互联网档案馆）
  - (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: 1_n1)
Norman Johnson Uniform Polytopes, Manuscript (1991)
- N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966)
2. Convex uniform polychora based on the tesseract (8-cell) and hexadecachoron (16-cell) - Models 13, 16, 17, George Olshevsky.
Klitzing, Richard. 4D uniform polytopes (polychora). bendwavy.org. o3o3o4o - tat, o3x3x4o - tah, x3x3o4o - thex

外部链接

Paper model of truncated tesseract （页面存档备份，存于互联网档案馆） created using nets generated by Stella4D software