| 释义 |
- Stericated 6-simplex Alternate names Coordinates Images
- Steritruncated 6-simplex Alternate names Coordinates Images
- Stericantellated 6-simplex Alternate names Coordinates Images
- Stericantitruncated 6-simplex Alternate names Coordinates Images
- Steriruncinated 6-simplex Alternate names Coordinates Images
- Steriruncitruncated 6-simplex Alternate names Coordinates Images
- Steriruncicantellated 6-simplex Alternate names Coordinates Images
- Steriruncicantitruncated 6-simplex Alternate names Coordinates Images
- Related uniform 6-polytopes
- Notes
- References
- External links
6-simplex
{{CDD>node_1|3|node|3|node|3|node|3|node|3|node}} | Stericated 6-simplex
{{CDD>node_1|3|node|3|node|3|node|3|node_1|3|node}} | Steritruncated 6-simplex
{{CDD>node_1|3|node_1|3|node|3|node|3|node_1|3|node}} | Stericantellated 6-simplex
{{CDD>node_1|3|node|3|node_1|3|node|3|node_1|3|node}} | Stericantitruncated 6-simplex
{{CDD>node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}} | Steriruncinated 6-simplex
{{CDD>node_1|3|node|3|node|3|node_1|3|node_1|3|node}} | Steriruncitruncated 6-simplex
{{CDD>node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}} | Steriruncicantellated 6-simplex
{{CDD>node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}} | Steriruncicantitruncated 6-simplex
{{CDD>node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}} | | Orthogonal projections in A6 Coxeter plane |
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In six-dimensional geometry, a stericated 6-simplex is a convex uniform 6-polytope with 4th order truncations (sterication) of the regular 6-simplex. There are 8 unique sterications for the 6-simplex with permutations of truncations, cantellations, and runcinations. Stericated 6-simplex | Stericated 6-simplex | | Type | uniform 6-polytope | | Schläfli symbol | t0,4{3,3,3,3,3} | | Coxeter-Dynkin diagrams | node_1|3|node|3|node|3|node_1|3|node|3|node}} | | 5-faces | 105 | | 4-faces | 700 | | Cells | 1470 | | Faces | 1400 | | Edges | 630 | | Vertices | 105 | | Vertex figure | | Coxeter group | A6, [35], order 5040 | | Properties | convex |
Alternate names - Small cellated heptapeton (Acronym: scal) (Jonathan Bowers)[1]
Coordinates The vertices of the stericated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,1,1,1,1,2). This construction is based on facets of the stericated 7-orthoplex. Images {{6-simplex Coxeter plane graphs|t04|150}}Steritruncated 6-simplex| Steritruncated 6-simplex | | Type | uniform 6-polytope | | Schläfli symbol | t0,1,4{3,3,3,3,3} | | Coxeter-Dynkin diagrams | node_1|3|node_1|3|node|3|node|3|node_1|3|node}} | | 5-faces | 105 | | 4-faces | 945 | | Cells | 2940 | | Faces | 3780 | | Edges | 2100 | | Vertices | 420 | | Vertex figure | | Coxeter group | A6, [35], order 5040 | | Properties | convex |
Alternate names - Cellirhombated heptapeton (Acronym: catal) (Jonathan Bowers)[2]
Coordinates The vertices of the steritruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,1,1,1,2,3). This construction is based on facets of the steritruncated 7-orthoplex. Images {{6-simplex Coxeter plane graphs|t014|150}}Stericantellated 6-simplex| Stericantellated 6-simplex | | Type | uniform 6-polytope | | Schläfli symbol | t0,2,4{3,3,3,3,3} | | Coxeter-Dynkin diagrams | node_1|3|node|3|node_1|3|node|3|node_1|3|node}} | | 5-faces | 105 | | 4-faces | 1050 | | Cells | 3465 | | Faces | 5040 | | Edges | 3150 | | Vertices | 630 | | Vertex figure | | Coxeter group | A6, [35], order 5040 | | Properties | convex |
Alternate names - Cellirhombated heptapeton (Acronym: cral) (Jonathan Bowers)[3]
Coordinates The vertices of the stericantellated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,1,1,2,2,3). This construction is based on facets of the stericantellated 7-orthoplex. Images {{6-simplex Coxeter plane graphs|t024|150}}Stericantitruncated 6-simplex| stericantitruncated 6-simplex | | Type | uniform 6-polytope | | Schläfli symbol | t0,1,2,4{3,3,3,3,3} | | Coxeter-Dynkin diagrams | node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}} | | 5-faces | 105 | | 4-faces | 1155 | | Cells | 4410 | | Faces | 7140 | | Edges | 5040 | | Vertices | 1260 | | Vertex figure | | Coxeter group | A6, [35], order 5040 | | Properties | convex |
Alternate names - Celligreatorhombated heptapeton (Acronym: cagral) (Jonathan Bowers)[4]
Coordinates The vertices of the stericanttruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,0,1,2,3,4). This construction is based on facets of the stericantitruncated 7-orthoplex. Images {{6-simplex Coxeter plane graphs|t0124|150}}Steriruncinated 6-simplex| steriruncinated 6-simplex | | Type | uniform 6-polytope | | Schläfli symbol | t0,3,4{3,3,3,3,3} | | Coxeter-Dynkin diagrams | node_1|3|node|3|node|3|node_1|3|node_1|3|node}} | | 5-faces | 105 | | 4-faces | 700 | | Cells | 1995 | | Faces | 2660 | | Edges | 1680 | | Vertices | 420 | | Vertex figure | | Coxeter group | A6, [35], order 5040 | | Properties | convex |
Alternate names - Celliprismated heptapeton (Acronym: copal) (Jonathan Bowers)[5]
Coordinates The vertices of the steriruncinated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,1,2,2,3,3). This construction is based on facets of the steriruncinated 7-orthoplex. Images {{6-simplex Coxeter plane graphs|t034|150}}Steriruncitruncated 6-simplex| steriruncitruncated 6-simplex | | Type | uniform 6-polytope | | Schläfli symbol | t0,1,3,4{3,3,3,3,3} | | Coxeter-Dynkin diagrams | node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}} | | 5-faces | 105 | | 4-faces | 945 | | Cells | 3360 | | Faces | 5670 | | Edges | 4410 | | Vertices | 1260 | | Vertex figure | | Coxeter group | A6, [35], order 5040 | | Properties | convex |
Alternate names - Celliprismatotruncated heptapeton (Acronym: captal) (Jonathan Bowers)[6]
Coordinates The vertices of the steriruncittruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,0,1,2,3,4). This construction is based on facets of the steriruncitruncated 7-orthoplex. Images {{6-simplex Coxeter plane graphs|t0134|150}}Steriruncicantellated 6-simplex| steriruncicantellated 6-simplex | | Type | uniform 6-polytope | | Schläfli symbol | t0,2,3,4{3,3,3,3,3} | | Coxeter-Dynkin diagrams | node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}} | | 5-faces | 105 | | 4-faces | 1050 | | Cells | 3675 | | Faces | 5880 | | Edges | 4410 | | Vertices | 1260 | | Vertex figure | | Coxeter group | A6, [35], order 5040 | | Properties | convex |
Alternate names - Bistericantitruncated 6-simplex as t1,2,3,5{3,3,3,3,3}
- Celliprismatorhombated heptapeton (Acronym: copril) (Jonathan Bowers)[7]
Coordinates The vertices of the steriruncitcantellated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,0,1,2,3,4). This construction is based on facets of the steriruncicantellated 7-orthoplex. Images {{6-simplex Coxeter plane graphs|t0234|150}}Steriruncicantitruncated 6-simplex| Steriuncicantitruncated 6-simplex | | Type | uniform 6-polytope | | Schläfli symbol | t0,1,2,3,4{3,3,3,3,3} | | Coxeter-Dynkin diagrams | node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}} | | 5-faces | 105 | | 4-faces | 1155 | | Cells | 4620 | | Faces | 8610 | | Edges | 7560 | | Vertices | 2520 | | Vertex figure | | Coxeter group | A6, [35], order 5040 | | Properties | convex |
Alternate names - Great cellated heptapeton (Acronym: gacal) (Jonathan Bowers)[8]
Coordinates The vertices of the steriruncicantittruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,1,2,3,4,5). This construction is based on facets of the steriruncicantitruncated 7-orthoplex. Images {{6-simplex Coxeter plane graphs|t01234|150}} Related uniform 6-polytopes The truncated 6-simplex is one of 35 uniform 6-polytopes based on the [3,3,3,3,3] Coxeter group, all shown here in A6 Coxeter plane orthographic projections. {{Heptapeton family}} Notes1. ^Klitzing, (x3o3o3o3x3o - scal)
2. ^Klitzing, (x3x3o3o3x3o - catal)
3. ^Klitzing, (x3o3x3o3x3o - cral)
4. ^Klitzing, (x3x3x3o3x3o - cagral)
5. ^Klitzing, (x3o3o3x3x3o - copal)
6. ^Klitzing, (x3x3o3x3x3o - captal)
7. ^Klitzing, ( x3o3x3x3x3o - copril)
8. ^Klitzing, (x3x3x3x3x3o - gacal)
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 |