| 释义 |
- Runcinated 8-simplex Alternate names Coordinates Images
- Biruncinated 8-simplex Alternate names Coordinates Images
- Triruncinated 8-simplex Alternate names Coordinates Images
- Runcitruncated 8-simplex Images
- Biruncitruncated 8-simplex Images
- Triruncitruncated 8-simplex Images
- Runcicantellated 8-simplex Images
- Biruncicantellated 8-simplex Images
- Runcicantitruncated 8-simplex Images
- Biruncicantitruncated 8-simplex Images
- Triruncicantitruncated 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}} | Runcinated 8-simplex
{{CDD>node_1|3|node|3|node|3|node_1|3|node|3|node|3|node|3|node}} | Biruncinated 8-simplex
{{CDD>node|3|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node}} | Triruncinated 8-simplex
{{CDD>node|3|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node}} | Runcitruncated 8-simplex
{{CDD>node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node}} | Biruncitruncated 8-simplex
{{CDD>node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node}} | Triruncitruncated 8-simplex
{{CDD>node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node}} | Runcicantellated 8-simplex
{{CDD>node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node}} | Biruncicantellated 8-simplex
{{CDD>node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node}} | Runcicantitruncated 8-simplex
{{CDD>node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node}} | Biruncicantitruncated 8-simplex
{{CDD>node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}} | Triruncicantitruncated 8-simplex
{{CDD>node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}} | | Orthogonal projections in A8 Coxeter plane |
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In eight-dimensional geometry, a runcinated 8-simplex is a convex uniform 8-polytope with 3rd order truncations (runcination) of the regular 8-simplex. There are eleven unique runcinations of the 8-simplex, including permutations of truncation and cantellation. The triruncinated 8-simplex and triruncicantitruncated 8-simplex have a doubled symmetry, showing [18] order reflectional symmetry in the A8 Coxeter plane. Runcinated 8-simplex| Runcinated 8-simplex | | Type | uniform 8-polytope | | Schläfli symbol | t0,3{3,3,3,3,3,3,3} | | Coxeter-Dynkin diagrams | node_1|3|node|3|node|3|node_1|3|node|3|node|3|node|3|node}} | | 6-faces | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | 4536 | | Vertices | 504 | | Vertex figure | | Coxeter group | A8, [37], order 362880 | | Properties | convex |
Alternate names - Runcinated enneazetton
- Small prismated enneazetton (Acronym: spene) (Jonathan Bowers)[1]
Coordinates The Cartesian coordinates of the vertices of the runcinated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,1,1,1,2). This construction is based on facets of the runcinated 9-orthoplex. Images {{8-simplex Coxeter plane graphs|t03|120px}} Biruncinated 8-simplex | Biruncinated 8-simplex | | Type | uniform 8-polytope | | Schläfli symbol | t1,4{3,3,3,3,3,3,3} | | Coxeter-Dynkin diagram | node|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 | 11340 | | Vertices | 1260 | | Vertex figure | | Coxeter group | A8, [37], order 362880 | | Properties | convex |
Alternate names - Biruncinated enneazetton
- Small biprismated enneazetton (Acronym: sabpene) (Jonathan Bowers)[2]
Coordinates The Cartesian coordinates of the vertices of the biruncinated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,1,1,1,2,2). This construction is based on facets of the biruncinated 9-orthoplex. Images {{8-simplex Coxeter plane graphs|t14|120px}} Triruncinated 8-simplex | Triruncinated 8-simplex | | Type | uniform 8-polytope | | Schläfli symbol | t2,5{3,3,3,3,3,3,3} | | Coxeter-Dynkin diagrams | node|3|node|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 | 15120 | | Vertices | 1680 | | Vertex figure | | Coxeter group | A8×2, [[37]], order 725760 | | Properties | convex |
Alternate names - Triruncinated enneazetton
- Small triprismated enneazetton (Acronym: satpeb) (Jonathan Bowers)[3]
Coordinates The Cartesian coordinates of the vertices of the triruncinated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,1,1,1,2,2,2). This construction is based on facets of the triruncinated 9-orthoplex. Images {{8-simplex2 Coxeter plane graphs|t25|120px}}Runcitruncated 8-simplex{{CDD|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node}} Images {{8-simplex2 Coxeter plane graphs|t013|120px}}Biruncitruncated 8-simplex{{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node}} Images {{8-simplex2 Coxeter plane graphs|t124|120px}}Triruncitruncated 8-simplex{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node}} Images {{8-simplex2 Coxeter plane graphs|t235|120px}}Runcicantellated 8-simplex{{CDD|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node}} Images {{8-simplex2 Coxeter plane graphs|t023|120px}}Biruncicantellated 8-simplex{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node}} Images {{8-simplex2 Coxeter plane graphs|t134|120px}}Runcicantitruncated 8-simplex{{CDD|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node}} Images {{8-simplex2 Coxeter plane graphs|t0123|120px}}Biruncicantitruncated 8-simplex{{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}} Images {{8-simplex2 Coxeter plane graphs|t1234|120px}}Triruncicantitruncated 8-simplex{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}} Images {{8-simplex2 Coxeter plane graphs|t2345|120px}} Related polytopes This polytope is one of 135 uniform 8-polytopes with A8 symmetry. {{Enneazetton family}} Notes 1. ^Klitzing (x3o3o3x3o3o3o3o - spene)
2. ^Klitzing (o3x3o3o3x3o3o3o - sabpene)
3. ^Klitzing (o3o3x3o3o3x3o3o - satpeb)
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)}} x3o3o3x3o3o3o3o - spene, o3x3o3o3x3o3o3o - sabpene, o3o3x3o3o3x3o3o - satpeb
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 |