過截角正五胞體
過截角正五胞體 | |
---|---|
類型 | 均勻多胞體 |
識別 | |
名稱 | 過截角正五胞體 |
參考索引 | 5 6 7 |
數學表示法 | |
考克斯特符號 | or |
施萊夫利符號 | t1,2{3,3,3} |
性質 | |
胞 | 10 (3.6.6) |
面 | 20 {3} 20 {6} |
邊 | 60 |
頂點 | 30 |
組成與佈局 | |
頂點圖 | (鍥形體) |
對稱性 | |
考克斯特群 | A4, [[3,3,3]], order 240 |
特性 | |
convex, isogonal isotoxal, isochoric | |
過截角正五胞體(又叫正十胞體)是一個四維多胞體, 由10個相同的三維胞截角四面體組成。每條邊連接到兩個六邊形和一個三角形。
過截角正五胞體的五維類比是過截角五維正六胞體。它的n維類比的考克斯特-迪金點圖都是中間的一個或兩個點有環。
過截角正五胞體是兩個由一種三維胞所組成的半正多胞體之一。另一個是過截角正二十四胞體,它由48個截角立方體組成。
投影
Ak 考克斯特平面 |
A4 | A3 | A2 |
---|---|---|---|
Graph | |||
二面體群 | [5] | [4] | [3] |
球極投影 (對着一個六邊形面) |
展開圖 |
坐標
一個棱長為2的過截角正五胞體的20個頂點的笛卡兒坐標系坐標
|
更簡單的,過截角正五胞體的頂點是五維空間笛卡兒坐標系的(0,0,1,2,2)或(1,0,0,0,-1)的全排列。
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