过截角正二十四胞体 - 维基百科，自由的百科全书

过截角正二十四胞体
过截角正二十四胞体
	施莱格尔投影
類型	均匀多胞体
識別
名稱	过截角正二十四胞体
參考索引	5 6 7
數學表示法
考克斯特符號; （英语：Coxeter-Dynkin diagram）	; or
施萊夫利符號	t1,2{3,4,3}
性質
胞	48 (3.8.8)
面	336; 192 {3}; 144 {8}
邊	576
頂點	288
組成與佈局
顶点图	; (锲形体)
對稱性
考克斯特群	F4, [[3,4,3]], order 2304
特性
	convex, isogonal isotoxal, isochoric
	查; 论; 编;

过截角正二十四胞体（又叫正四十八胞体）是一个四维多胞体, 由48个相同的三维胞截角立方体组成。每条边连接到两个八边形和一个三角形。

过截角正二十四胞体是两个由一种三维胞所组成的半正多胞体之一。另一个是过截角正五胞体，它由10个截角四面体组成。

投影

正射投影
A_k 考克斯特平面	A₄	A₃	A₂
Graph
二面体群	[5]	[4]	[3]

球极投影 (对着一个八边形面)	展开图

一个棱长为2的过截角正二十四胞体的288个顶点的笛卡儿坐标系坐标

\pm \left({\sqrt {\frac {5}{2}}},\ {\frac {5}{\sqrt {6}}},\ {\frac {2}{\sqrt {3}}},\ 0\right)

\pm \left({\sqrt {\frac {5}{2}}},\ {\frac {5}{\sqrt {6}}},\ {\frac {-1}{\sqrt {3}}},\ \pm 1\right)

\pm \left({\sqrt {\frac {5}{2}}},\ {\frac {1}{\sqrt {6}}},\ {\frac {4}{\sqrt {3}}},\ 0\right)

\pm \left({\sqrt {\frac {5}{2}}},\ {\frac {1}{\sqrt {6}}},\ {\frac {-2}{\sqrt {3}}},\ \pm 2\right)

\pm \left({\sqrt {\frac {5}{2}}},\ -{\sqrt {\frac {3}{2}}},\ \pm {\sqrt {3}},\ \pm 1\right)

\pm \left({\sqrt {\frac {5}{2}}},\ -{\sqrt {\frac {3}{2}}},\ 0,\ \pm 2\right)

\pm \left(0,\ 2{\sqrt {\frac {2}{3}}},\ {\frac {4}{\sqrt {3}}},\ 0\right)

\pm \left(0,\ 2{\sqrt {\frac {2}{3}}},\ {\frac {-2}{\sqrt {3}}},\ \pm 2\right)

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] （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]
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 icosittrachoron - Model 3, George Olshevsky.
Klitzing, Richard. 4D uniform polytopes (polychora). bendwavy.org. x3x3o3o - tip, o3x3x3o - deca