截角超立方體
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截角超立方体 | |
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類型 | 均匀多胞体 |
識別 | |
名稱 | 截角超立方体 |
參考索引 | 12 13 14 |
數學表示法 | |
考克斯特符號 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
施萊夫利符號 | t0,1{4,3,3} |
性質 | |
胞 | 24 8 3.8.8 ![]() 16 3.3.3 ![]() |
面 | 88 64 {3} 24 {8} |
邊 | 128 |
頂點 | 64 |
組成與佈局 | |
顶点图 | ![]() Isosceles triangular pyramid |
對稱性 | |
考克斯特群 | BC4, [4,3,3], order 384 |
特性 | |
convex | |
坐标
截角超立方体可以通过在每条棱距离顶点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:
投影
考克斯特平面 | B4 | B3 / D4 / A2 | B2 / D3 |
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Graph | ![]() |
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二面体群 | [8] | [6] | [4] |
考克斯特平面 | F4 | A3 | |
Graph | ![]() |
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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: 1n1)
- 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