| 释义 |
- Stericated 6-cube Alternate names Images
- Steritruncated 6-cube Alternate names Images
- Stericantellated 6-cube Alternate names Images
- Stericantitruncated 6-cube Alternate names Images
- Steriruncinated 6-cube Alternate names Images
- Steriruncitruncated 6-cube Alternate names Images
- Steriruncicantellated 6-cube Alternate names Images
- Steriruncicantitruncated 6-cube Alternate names Images
- Related polytopes
- Notes
- References
- External links
6-cube
{{CDD>node_1|4|node|3|node|3|node|3|node|3|node}} | Stericated 6-cube
{{CDD>node_1|4|node|3|node|3|node|3|node_1|3|node}} | Steritruncated 6-cube
{{CDD>node_1|4|node_1|3|node|3|node|3|node_1|3|node}} | Stericantellated 6-cube
{{CDD>node_1|4|node|3|node_1|3|node|3|node_1|3|node}} | Stericantitruncated 6-cube
{{CDD>node_1|4|node_1|3|node_1|3|node|3|node_1|3|node}} | Steriruncinated 6-cube
{{CDD>node_1|4|node|3|node|3|node_1|3|node_1|3|node}} | Steriruncitruncated 6-cube
{{CDD>node_1|4|node_1|3|node|3|node_1|3|node_1|3|node}} | Steriruncicantellated 6-cube
{{CDD>node_1|4|node|3|node_1|3|node_1|3|node_1|3|node}} | Steriruncicantitruncated 6-cube
{{CDD>node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node}} | | Orthogonal projections in B6 Coxeter plane |
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In six-dimensional geometry, a stericated 6-cube is a convex uniform 6-polytope, constructed as a sterication (4th order truncation) of the regular 6-cube. There are 8 unique sterications for the 6-cube with permutations of truncations, cantellations, and runcinations. Stericated 6-cube | Stericated 6-cube | | Type | uniform 6-polytope | | Schläfli symbol | 2r2r{4,3,3,3,3} | | Coxeter-Dynkin diagrams | node_1|4|node|3|node|3|node|3|node_1|3|node}}
{{CDD|node|split1|nodes|3a4b|nodes_11|3a|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 hexeract (Acronym: scox) (Jonathan Bowers)[1]
Images {{6-cube Coxeter plane graphs|t04|150}}Steritruncated 6-cube| Steritruncated 6-cube | | Type | uniform 6-polytope | | Schläfli symbol | t0,1,4{4,3,3,3,3} | | Coxeter-Dynkin diagrams | node_1|4|node_1|3|node|3|node|3|node_1|3|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 - Cellirhombated hexeract (Acronym: catax) (Jonathan Bowers)[2]
Images {{6-cube Coxeter plane graphs|t014|150}}Stericantellated 6-cube| Stericantellated 6-cube | | Type | uniform 6-polytope | | Schläfli symbol | 2r2r{4,3,3,3,3} | | Coxeter-Dynkin diagrams | node_1|4|node|3|node_1|3|node|3|node_1|3|node}}
{{CDD|node_1|split1|nodes|3a4b|nodes_11|3a|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 hexeract (Acronym: crax) (Jonathan Bowers)[3]
Images {{6-cube Coxeter plane graphs|t024|150}}Stericantitruncated 6-cube| stericantitruncated 6-cube | | Type | uniform 6-polytope | | Schläfli symbol | t0,1,2,4{4,3,3,3,3} | | Coxeter-Dynkin diagrams | node_1|4|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 hexeract (Acronym: cagorx) (Jonathan Bowers)[4]
Images {{6-cube Coxeter plane graphs|t0124|150}}Steriruncinated 6-cube| steriruncinated 6-cube | | Type | uniform 6-polytope | | Schläfli symbol | t0,3,4{4,3,3,3,3} | | Coxeter-Dynkin diagrams | node_1|4|node|3|node|3|node_1|3|node_1|3|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 hexeract (Acronym: copox) (Jonathan Bowers)[5]
Images {{6-cube Coxeter plane graphs|t034|150}}Steriruncitruncated 6-cube| steriruncitruncated 6-cube | | Type | uniform 6-polytope | | Schläfli symbol | 2t2r{4,3,3,3,3} | | Coxeter-Dynkin diagrams | node_1|4|node_1|3|node|3|node_1|3|node_1|3|node}}
{{CDD|node|split1|nodes_11|3a4b|nodes_11|3a|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 hexeract (Acronym: captix) (Jonathan Bowers)[6]
Images {{6-cube Coxeter plane graphs|t0134|150}}Steriruncicantellated 6-cube| steriruncicantellated 6-cube | | Type | uniform 6-polytope | | Schläfli symbol | t0,2,3,4{4,3,3,3,3} | | Coxeter-Dynkin diagrams | node_1|4|node|3|node_1|3|node_1|3|node_1|3|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 hexeract (Acronym: coprix) (Jonathan Bowers)[7]
Images {{6-cube Coxeter plane graphs|t0234|150}}Steriruncicantitruncated 6-cube| Steriuncicantitruncated 6-cube | | Type | uniform 6-polytope | | Schläfli symbol | tr2r{4,3,3,3,3} | | Coxeter-Dynkin diagrams | node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node}}
{{CDD|node_1|split1|nodes_11|3a4b|nodes_11|3a|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 hexeract (Acronym: gocax) (Jonathan Bowers)[8]
Images {{6-cube Coxeter plane graphs|t01234|150}} Related polytopesThese polytopes are from a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex. {{Hexeract family}} Notes1. ^Klitzing, (x4o3o3o3x3o - scox)
2. ^Klitzing, (x4x3o3o3x3o - catax)
3. ^Klitzing, (x4o3x3o3x3o - crax)
4. ^Klitzing, (x4x3x3o3x3o - cagorx)
5. ^Klitzing, (x4o3o3x3x3o - copox))
6. ^Klitzing, (x4x3o3x3x3o - captix)
7. ^Klitzing, (x4o3x3x3x3o - coprix)
8. ^Klitzing, (x4x3x3x3x3o - gocax)
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 |