| 释义 |
- Coordinates
- Images
- Related polytopes
- Notes
- References
- External links
| 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 | node_1|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node}} | | 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 {{8-simplex Coxeter plane graphs|t06|120px}} Related polytopes This polytope is one of 135 uniform 8-polytopes with A8 symmetry. {{Enneazetton family}} 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}}
- (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
- {{KlitzingPolytopes|polyzetta.htm|8D uniform polytopes (polyzetta)|x3o3o3o3o3o3x3o}}
External links - [https://web.archive.org/web/20070310205351/http://members.cox.net/hedrondude/topes.htm Polytopes of Various Dimensions]
- Multi-dimensional Glossary
{{Polytopes}} 1 : 8-polytopes |