| 释义 |
- Stericated 6-orthoplex Alternate names Images
- Steritruncated 6-orthoplex Alternate names Images
- Stericantellated 6-orthoplex Alternate names Images
- Stericantitruncated 6-orthoplex Alternate names Images
- Steriruncinated 6-orthoplex Alternate names Images
- Steriruncitruncated 6-orthoplex Alternate names Images
- Steriruncicantellated 6-orthoplex Alternate names Images
- Steriruncicantitruncated 6-orthoplex Alternate names Images
- Related polytopes
- Notes
- References
- External links
6-orthoplex
{{CDD>node_1|3|node|3|node|3|node|3|node|4|node}} | Stericated 6-orthoplex
{{CDD>node_1|3|node|3|node|3|node|3|node_1|4|node}} | Steritruncated 6-orthoplex
{{CDD>node_1|3|node_1|3|node|3|node|3|node_1|4|node}} | Stericantellated 6-orthoplex
{{CDD>node_1|3|node|3|node_1|3|node|3|node_1|4|node}} | Stericantitruncated 6-orthoplex
{{CDD>node_1|3|node_1|3|node_1|3|node|3|node_1|4|node}} | Steriruncinated 6-orthoplex
{{CDD>node_1|3|node|3|node|3|node_1|3|node_1|4|node}} | Steriruncitruncated 6-orthoplex
{{CDD>node_1|3|node_1|3|node|3|node_1|3|node_1|4|node}} | Steriruncicantellated 6-orthoplex
{{CDD>node_1|3|node|3|node_1|3|node_1|3|node_1|4|node}} | Steriruncicantitruncated 6-orthoplex
{{CDD>node_1|3|node_1|3|node_1|3|node_1|3|node_1|4|node}} | | Orthogonal projections in B6 Coxeter plane |
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In six-dimensional geometry, a stericated 6-orthoplex is a convex uniform 6-polytope, constructed as a sterication (4th order truncation) of the regular 6-orthoplex. There are 16 unique sterications for the 6-orthoplex with permutations of truncations, cantellations, and runcinations. Eight are better represented from the stericated 6-cube. Stericated 6-orthoplex | Stericated 6-orthoplex | | Type | uniform 6-polytope | | Schläfli symbol | 2r2r{3,3,3,3,4} | | Coxeter-Dynkin diagrams | node_1|3|node|3|node|3|node|3|node_1|4|node}}
{{CDD|node|split1|nodes|3ab|nodes_11|4a|nodea}} | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | 5760 | | Vertices | 960 | | Vertex figure | | Coxeter groups | B6, [4,3,3,3,3] | | Properties | convex |
Alternate names - Small cellated hexacontatetrapeton (Acronym: scag) (Jonathan Bowers)[1]
Images {{6-cube Coxeter plane graphs|t15|150}}Steritruncated 6-orthoplex| Steritruncated 6-orthoplex | | Type | uniform 6-polytope | | Schläfli symbol | t0,1,4{3,3,3,3,4} | | Coxeter-Dynkin diagrams | node_1|3|node_1|3|node|3|node|3|node_1|4|node}} | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | 19200 | | Vertices | 3840 | | Vertex figure | | Coxeter groups | B6, [4,3,3,3,3] | | Properties | convex |
Alternate names - Cellitruncated hexacontatetrapeton (Acronym: catog) (Jonathan Bowers)[2]
Images {{6-cube Coxeter plane graphs|t145|150}}Stericantellated 6-orthoplex| Stericantellated 6-orthoplex | | Type | uniform 6-polytope | | Schläfli symbols | t0,2,4{34,4}
rr2r{3,3,3,3,4} | | Coxeter-Dynkin diagrams | node_1|3|node|3|node_1|3|node|3|node_1|4|node}}{{CDD|node_1|split1|nodes|3ab|nodes_11|4a|nodea}} | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | 28800 | | Vertices | 5760 | | Vertex figure | | Coxeter groups | B6, [4,3,3,3,3] | | Properties | convex |
Alternate names - Cellirhombated hexacontatetrapeton (Acronym: crag) (Jonathan Bowers)[3]
Images {{6-cube Coxeter plane graphs|t135|150}}Stericantitruncated 6-orthoplex| stericantitruncated 6-orthoplex | | Type | uniform 6-polytope | | Schläfli symbol | t0,1,2,4{3,3,3,3,4} | | Coxeter-Dynkin diagrams | node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}} | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | 46080 | | Vertices | 11520 | | Vertex figure | | Coxeter groups | B6, [4,3,3,3,3] | | Properties | convex |
Alternate names - Celligreatorhombated hexacontatetrapeton (Acronym: cagorg) (Jonathan Bowers)[4]
Images {{6-cube Coxeter plane graphs|t1345|150}}Steriruncinated 6-orthoplex| steriruncinated 6-orthoplex | | Type | uniform 6-polytope | | Schläfli symbol | t0,3,4{3,3,3,3,4} | | Coxeter-Dynkin diagrams | node_1|3|node|3|node|3|node_1|3|node_1|4|node}} | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | 15360 | | Vertices | 3840 | | Vertex figure | | Coxeter groups | B6, [4,3,3,3,3] | | Properties | convex |
Alternate names - Celliprismated hexacontatetrapeton (Acronym: copog) (Jonathan Bowers)[5]
Images {{6-cube Coxeter plane graphs|t125|150}}Steriruncitruncated 6-orthoplex| steriruncitruncated 6-orthoplex | | Type | uniform 6-polytope | | Schläfli symbol | 2t2r{3,3,3,3,4} | | Coxeter-Dynkin diagrams | node_1|3|node_1|3|node|3|node_1|3|node_1|4|node}}
{{CDD|node|split1|nodes_11|3ab|nodes_11|4a|nodea}} | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | 40320 | | Vertices | 11520 | | Vertex figure | | Coxeter groups | B6, [4,3,3,3,3] | | Properties | convex |
Alternate names - Celliprismatotruncated hexacontatetrapeton (Acronym: captog) (Jonathan Bowers)[6]
Images {{6-cube Coxeter plane graphs|t1245|150}}Steriruncicantellated 6-orthoplex| steriruncicantellated 6-orthoplex | | Type | uniform 6-polytope | | Schläfli symbol | t0,2,3,4{3,3,3,3,4} | | Coxeter-Dynkin diagrams | node_1|3|node|3|node_1|3|node_1|3|node_1|4|node}} | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | 40320 | | Vertices | 11520 | | Vertex figure | | Coxeter groups | B6, [4,3,3,3,3] | | Properties | convex |
Alternate names - Celliprismatorhombated hexacontatetrapeton (Acronym: coprag) (Jonathan Bowers)[7]
Images {{6-cube Coxeter plane graphs|t1235|150}}Steriruncicantitruncated 6-orthoplex| Steriuncicantitruncated 6-orthoplex | | Type | uniform 6-polytope | | Schläfli symbols | t0,1,2,3,4{34,4}
tr2r{3,3,3,3,4} | | Coxeter-Dynkin diagrams | node_1|3|node_1|3|node_1|3|node_1|3|node_1|4|node}}{{CDD|node_1|split1|nodes_11|3ab|nodes_11|4a|nodea}} | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | 69120 | | Vertices | 23040 | | Vertex figure | | Coxeter groups | B6, [4,3,3,3,3] | | Properties | convex |
Alternate names - Great cellated hexacontatetrapeton (Acronym: gocog) (Jonathan Bowers)[8]
Images {{6-cube Coxeter plane graphs|t12345|150}} Related polytopesThese polytopes are from a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-orthoplex or 6-orthoplex. {{Hexeract family}} Notes1. ^Klitzing, (x3o3o3o3x4o - scag)
2. ^Klitzing, (x3x3o3o3x4o - catog)
3. ^Klitzing, (x3o3x3o3x4o - crag)
4. ^Klitzing, (x3x3x3o3x4o - cagorg)
5. ^Klitzing, (x3o3o3x3x4o - copog)
6. ^Klitzing, (x3x3o3x3x4o - captog)
7. ^Klitzing, (x3o3x3x3x4o - coprag)
8. ^Klitzing, (x3x3x3x3x4o - gocog)
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|polypeta.htm|6D|uniform polytopes (polypeta)}}
External links - [https://web.archive.org/web/20070310205351/http://members.cox.net/hedrondude/topes.htm Polytopes of Various Dimensions]
- Multi-dimensional Glossary
{{Polytopes}} 1 : 6-polytopes |