| 释义 |
- Stericated 8-simplex Coordinates Images
- Bistericated 8-simplex Coordinates Images
- Steritruncated 8-simplex Images
- Bisteritruncated 8-simplex Images
- Stericantellated 8-simplex Images
- Bistericantellated 8-simplex Images
- Stericantitruncated 8-simplex Images
- Bistericantitruncated 8-simplex Images
- Steriruncinated 8-simplex Images
- Bisteriruncinated 8-simplex Images
- Steriruncitruncated 8-simplex Images
- Bisteriruncitruncated 8-simplex Images
- Steriruncicantellated 8-simplex Images
- Bisteriruncicantellated 8-simplex Images
- Steriruncicantitruncated 8-simplex Images
- Bisteriruncicantitruncated 8-simplex Images
- Related polytopes
- Notes
- References
- External links
8-simplex
{{CDD>node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node}} | Stericated 8-simplex
{{CDD>node_1|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node}} | Bistericated 8-simplex
{{CDD>node|3|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node}} | Steri-truncated 8-simplex
{{CDD>node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node}} | Bisteri-truncated 8-simplex
{{CDD>node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node}} | Steri-cantellated 8-simplex
{{CDD>node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node}} | Bisteri-cantellated 8-simplex
{{CDD>node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node}} | Stericanti-truncated 8-simplex
{{CDD>node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node}} | Bistericanti-truncated 8-simplex
{{CDD>node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node}} | Steri-runcinated 8-simplex
{{CDD>node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node}} | Bisteri-runcinated 8-simplex
{{CDD>node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node}} | Steriruncitruncated 8-simplex
{{CDD>node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node}} | Bisterirun-citruncated 8-simplex
{{CDD>node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}} | Sterirunci-cantellated 8-simplex
{{CDD>node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}} | Bisterirunci-cantellated 8-simplex
{{CDD>node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}} | Steriruncicanti-truncated 8-simplex
{{CDD>node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}} | Bisteriruncicanti-truncated 8-simplex
{{CDD>node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}} | | Orthogonal projections in A8 Coxeter plane |
|---|
In eight-dimensional geometry, a stericated 8-simplex is a convex uniform 8-polytope with 4th order truncations (sterication) of the regular 8-simplex. There are 16 unique sterications for the 8-simplex including permutations of truncation, cantellation, and runcination. Stericated 8-simplex {{-}}| Stericated 8-simplex | | Type | uniform 8-polytope | | Schläfli symbol | t0,4{3,3,3,3,3,3,3} | | Coxeter-Dynkin diagrams | node_1|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node}} | | 7-faces | | 6-faces | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | 6300 | | Vertices | 630 | | Vertex figure | | Coxeter group | A8, [37], order 362880 | | Properties | convex |
Coordinates The Cartesian coordinates of the vertices of the stericated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,1,1,1,1,2). This construction is based on facets of the stericated 9-orthoplex. Images {{8-simplex Coxeter plane graphs|t04|120px}} Bistericated 8-simplex | bistericated 8-simplex | | Type | uniform 8-polytope | | Schläfli symbol | t1,5{3,3,3,3,3,3,3} | | Coxeter-Dynkin diagrams | node|3|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node}} | | 7-faces | | 6-faces | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | 12600 | | Vertices | 1260 | | Vertex figure | | Coxeter group | A8, [37], order 362880 | | Properties | convex |
Coordinates The Cartesian coordinates of the vertices of the bistericated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,1,1,1,1,2,2). This construction is based on facets of the bistericated 9-orthoplex. Images {{8-simplex Coxeter plane graphs|t15|120px}}Steritruncated 8-simplex| Steritruncated 8-simplex | | Type | uniform 8-polytope | | Schläfli symbol | t0,1,4{3,3,3,3,3,3,3} | | Coxeter-Dynkin diagrams | node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node}} | | 7-faces | | 6-faces | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | | Vertices | | Vertex figure | | Coxeter group | A8, [37], order 362880 | | Properties | convex |
Images {{8-simplex Coxeter plane graphs|t014|120px}}{{-}}Bisteritruncated 8-simplex| Bisteritruncated 8-simplex | | Type | uniform 8-polytope | | Schläfli symbol | t1,2,5{3,3,3,3,3,3,3} | | Coxeter-Dynkin diagrams | node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node}} | | 7-faces | | 6-faces | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | | Vertices | | Vertex figure | | Coxeter group | A8, [37], order 362880 | | Properties | convex |
Images {{8-simplex Coxeter plane graphs|t125|120px}}Stericantellated 8-simplex{{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node}} Images {{8-simplex Coxeter plane graphs|t024|120px}}Bistericantellated 8-simplex{{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node}} Images {{8-simplex Coxeter plane graphs|t135|120px}}Stericantitruncated 8-simplex{{CDD|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node}} Images {{8-simplex Coxeter plane graphs|t0124|120px}}Bistericantitruncated 8-simplex{{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node}} Images {{8-simplex Coxeter plane graphs|t1235|120px}}Steriruncinated 8-simplex{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node}} Images {{8-simplex Coxeter plane graphs|t034|120px}}Bisteriruncinated 8-simplex{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node}} Images {{8-simplex Coxeter plane graphs|t145|120px}}Steriruncitruncated 8-simplex{{CDD|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node}} Images {{8-simplex Coxeter plane graphs|t0134|120px}}Bisteriruncitruncated 8-simplex{{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}} Images {{8-simplex Coxeter plane graphs|t1245|120px}}Steriruncicantellated 8-simplex{{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}} Images {{8-simplex Coxeter plane graphs|t0234|120px}}Bisteriruncicantellated 8-simplex{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}} Images {{8-simplex Coxeter plane graphs|t1345|120px}}Steriruncicantitruncated 8-simplex{{CDD|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}} Images {{8-simplex Coxeter plane graphs|t01234|120px}}Bisteriruncicantitruncated 8-simplex{{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}} Images {{8-simplex Coxeter plane graphs|t12345|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, Ph.D.
- {{KlitzingPolytopes|polyzetta.htm|8D|uniform polytopes (polyzetta)}} x3o3o3o3x3o3o3o, o3x3o3o3o3x3o3o
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 |