Hexicated 8-simplexes
| Hexicated 8-simplex | |
|---|---|
 Orthogonal projection on A8 Coxeter plane | |
| Type | uniform 8-polytope |
| Schläfli symbol | t0,6{3,3,3,3,3,3,3} |
| Coxeter-Dynkin diagrams |   
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| 7-faces | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 2268 |
| Vertices | 252 |
| Vertex figure | |
| Coxeter groups | A8, [37], order 362880 |
| Properties | convex |
In eight-dimensional geometry, a hexicated 8-simplex is a uniform 8-polytope, being a hexication (6th order truncation) of the regular 8-simplex.
Coordinates
The Cartesian coordinates of the vertices of the hexicated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,1,1,1,1,1,2). This construction is based on facets of the hexicated 9-orthoplex.
Images
| Ak Coxeter plane | A8 | A7 | A6 | A5 |
|---|---|---|---|---|
| Graph |
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| Dihedral symmetry | [9] | [8] | [7] | [6] |
| Ak Coxeter plane | A4 | A3 | A2 | |
| Graph | 
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| Dihedral symmetry | [5] | [4] | [3] |
Related polytopes
This polytope is one of 135 uniform 8-polytopes with A8 symmetry.
Notes
References
- H.S.M. Coxeter:
- H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
- Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]
- (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]
- Norman Johnson Uniform Polytopes, Manuscript (1991)
- N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, PhD
- Klitzing, Richard. "8D uniform polytopes (polyzetta) x3o3o3o3o3o3x3o".