截半正二十四胞體
| 截半正二十四胞體 | |
|---|---|
 | |
| 類型 | 均勻多胞體 |
| 識別 | |
| 名稱 | 截半正二十四胞體 |
| 參考索引 | 2 3 4 |
| 數學表示法 | |
| 考克斯特符號 |     |
| 施萊夫利符號 | t1{3,4,3} |
| 性質 | |
| 胞 | 10 24 (4.4.4)  24 (3.4.3.4)  |
| 面 | 240 144 {4} 96 {3} |
| 邊 | 288 |
| 頂點 | 96 |
| 組成與佈局 | |
| 頂點圖 |  Elongated triangular prism |
| 對稱性 | |
| 考克斯特群 | F4, [3,4,3], order 1152 |
| 特性 | |
| convex, isogonal | |
截半正二十四胞體由48個三維胞組成: 24個立方體, 和24個截半立方體。每個頂點周圍環繞着三個截半立方體和兩個立方體。
構造
截角正二十四胞體的細胞可以通過在正二十四胞體的棱的中點處截斷其頂點。截斷的24個正八面體變成新的截半立方體，並在原來的頂點處產生了24個新的立方體。
結合
截角八面體的三角形面彼此結合在一起，而它們的正方形面則連接到立方體。
投影
| Fk 考克斯特平面 |
F4 | B4 | B3 | B2 |
|---|---|---|---|---|
| Graph | 
|
|
| |
| 二面體群 | [12] | [6] | [8] | [4] |
注釋
參考文獻
- H.S.M. Coxeter:
- H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
- 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]
- Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999, ISBN 0-486-40919-8 p.88 (Chapter 5: Regular Skew Polyhedra in three and four dimensions and their topological analogues, Proceedings of the London Mathematics Society, Ser. 2, Vol 43, 1937.)
- Coxeter, H. S. M. Regular Skew Polyhedra in Three and Four Dimensions. Proc. London Math. Soc. 43, 33-62, 1937.
- Norman Johnson Uniform Polytopes, Manuscript (1991)
- N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966)
- Olshevsky, George, Pentachoron at Glossary for Hyperspace.
- 1. Convex uniform polychora based on the pentachoron - Model 3, George Olshevsky.
- Klitzing, Richard. 4D uniform polytopes (polychora). bendwavy.org. x3x3o3o - tip, o3x3x3o - deca