截角超立方體
截角超立方體 | |
---|---|
類型 | 均勻多胞體 |
識別 | |
名稱 | 截角超立方體 |
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 | |
頂點圖 | Isosceles triangular pyramid |
對稱性 | |
考克斯特群 | BC4, [4,3,3], order 384 |
特性 | |
convex | |
坐標
截角超立方體可以通過在每條棱距離頂點處截斷超立方體的每一個角來得到。每個截斷的角會產生一個正四面體。
一個棱長為2的截角超立方體的每個頂點的笛卡兒坐標系坐標為:
投影
考克斯特平面 | B4 | B3 / D4 / A2 | B2 / D3 |
---|---|---|---|
Graph | |||
二面體群 | [8] | [6] | [4] |
考克斯特平面 | F4 | A3 | |
Graph | |||
二面體群 | [12/3] | [4] |
展開圖 |
三維正交投影 |
參考文獻
- 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] (頁面存檔備份,存於網際網路檔案館)
- (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
外部連結
- Paper model of truncated tesseract (頁面存檔備份,存於網際網路檔案館) created using nets generated by Stella4D software