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Stericated 7-simplexes
| Orthogonal projections in A7 Coxeter plane |
|---|
In seven-dimensional geometry, a stericated 7-simplex is a convex uniform 7-polytope with 4th order truncations (sterication) of the regular 7-simplex.
There are 14 unique sterication for the 7-simplex with permutations of truncations, cantellations, and runcinations.
Stericated 7-simplex
| Stericated 7-simplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter-Dynkin diagrams |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter group |
| Properties |
Alternate names
- Small cellated octaexon (acronym: sco) (Jonathan Bowers)
Coordinates
The vertices of the stericated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,1,1,1,2). This construction is based on facets of the stericated 8-orthoplex.
Images
Bistericated 7-simplex
| Bistericated 7-simplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter-Dynkin diagrams |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter group |
| Properties |
Alternate names
- Small bicellated hexadecaexon (acronym: sabach) (Jonathan Bowers)
Coordinates
The vertices of the bistericated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,1,1,2,2). This construction is based on facets of the bistericated 8-orthoplex.
Images
Steritruncated 7-simplex
| Steritruncated 7-simplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter-Dynkin diagrams |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter group |
| Properties |
Alternate names
- Cellitruncated octaexon (acronym: cato) (Jonathan Bowers)
Coordinates
The vertices of the steritruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,1,1,2,3). This construction is based on facets of the steritruncated 8-orthoplex.
Images
Bisteritruncated 7-simplex
| Bisteritruncated 7-simplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter-Dynkin diagrams |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter group |
| Properties |
Alternate names
- Bicellitruncated octaexon (acronym: bacto) (Jonathan Bowers)
Coordinates
The vertices of the bisteritruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,1,2,3,3). This construction is based on facets of the bisteritruncated 8-orthoplex.
Images
Stericantellated 7-simplex
| Stericantellated 7-simplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter-Dynkin diagrams |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter group |
| Properties |
Alternate names
- Cellirhombated octaexon (acronym: caro) (Jonathan Bowers)
Coordinates
The vertices of the stericantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,1,2,2,3). This construction is based on facets of the stericantellated 8-orthoplex.
Images
Bistericantellated 7-simplex
| Bistericantellated 7-simplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter-Dynkin diagrams |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter group |
| Properties |
Alternate names
- Bicellirhombihexadecaexon (acronym: bacroh) (Jonathan Bowers)
Coordinates
The vertices of the bistericantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,2,2,3,3). This construction is based on facets of the stericantellated 8-orthoplex.
Images
Stericantitruncated 7-simplex
| Stericantitruncated 7-simplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter-Dynkin diagrams |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter group |
| Properties |
Alternate names
- Celligreatorhombated octaexon (acronym: cagro) (Jonathan Bowers)
Coordinates
The vertices of the stericantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,1,2,3,4). This construction is based on facets of the stericantitruncated 8-orthoplex.
Images
Bistericantitruncated 7-simplex
| Bistericantitruncated 7-simplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter-Dynkin diagrams |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter group |
| Properties |
Alternate names
- Bicelligreatorhombated octaexon (acronym: bacogro) (Jonathan Bowers)
Coordinates
The vertices of the bistericantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,2,3,4,4). This construction is based on facets of the bistericantitruncated 8-orthoplex.
Images
Steriruncinated 7-simplex
| Steriruncinated 7-simplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter-Dynkin diagrams |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter group |
| Properties |
Alternate names
- Celliprismated octaexon (acronym: cepo) (Jonathan Bowers)
Coordinates
The vertices of the steriruncinated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,2,2,2,3). This construction is based on facets of the steriruncinated 8-orthoplex.
Images
Steriruncitruncated 7-simplex
| Steriruncitruncated 7-simplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter-Dynkin diagrams |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter group |
| Properties |
Alternate names
- Celliprismatotruncated octaexon (acronym: capto) (Jonathan Bowers)
Coordinates
The vertices of the steriruncitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,2,2,3,4). This construction is based on facets of the steriruncitruncated 8-orthoplex.
Images
Steriruncicantellated 7-simplex
| Steriruncicantellated 7-simplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter-Dynkin diagrams |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter group |
| Properties |
Alternate names
- Celliprismatorhombated octaexon (acronym: capro) (Jonathan Bowers)
Coordinates
The vertices of the steriruncicantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,2,3,3,4). This construction is based on facets of the steriruncicantellated 8-orthoplex.
Images
Bisteriruncitruncated 7-simplex
| Bisteriruncitruncated 7-simplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter-Dynkin diagrams |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter group |
| Properties |
Alternate names
- Bicelliprismatotruncated hexadecaexon (acronym: bicpath) (Jonathan Bowers)
Coordinates
The vertices of the bisteriruncitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,2,2,3,4,4). This construction is based on facets of the bisteriruncitruncated 8-orthoplex.
Images
Steriruncicantitruncated 7-simplex
| Steriruncicantitruncated 7-simplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter-Dynkin diagrams |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter group |
| Properties |
Alternate names
- Great cellated octaexon (acronym: gecco) (Jonathan Bowers)
Coordinates
The vertices of the steriruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,2,3,4,5). This construction is based on facets of the steriruncicantitruncated 8-orthoplex.
Images
Bisteriruncicantitruncated 7-simplex
| Bisteriruncicantitruncated 7-simplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter-Dynkin diagrams |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter group |
| Properties |
Alternate names
- Great bicellated hexadecaexon (gabach) (Jonathan Bowers)
Coordinates
The vertices of the bisteriruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,2,3,4,5,5). This construction is based on facets of the bisteriruncicantitruncated 8-orthoplex.
Images
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, wiley.com,
- (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.
- x3o3o3o3x3o3o - sco, o3x3o3o3o3x3o - sabach, x3x3o3o3x3o3o - cato, o3x3x3o3o3x3o - bacto, x3o3x3o3x3o3o - caro, o3x3o3x3o3x3o - bacroh, x3x3x3o3x3o3o - cagro, o3x3x3x3o3x3o - bacogro, x3o3o3x3x3o3o - cepo, x3x3x3o3x3o3o - capto, x3o3x3x3x3o3o - capro, o3x3x3o3x3x3o - bicpath, x3x3x3x3x3o3o - gecco, o3x3x3x3x3x3o - gabach
References
- Klitizing, (x3o3o3o3x3o3o - sco)
- Klitizing, (o3x3o3o3o3x3o - sabach)
- Klitizing, (x3x3o3o3x3o3o - cato)
- Klitizing, (o3x3x3o3o3x3o - bacto)
- Klitizing, (x3o3x3o3x3o3o - caro)
- Klitizing, (o3x3o3x3o3x3o - bacroh)
- Klitizing, (x3x3x3o3x3o3o - cagro)
- Klitizing, (o3x3x3x3o3x3o - bacogro)
- Klitizing, (x3o3o3x3x3o3o - cepo)
- Klitizing, (x3x3x3o3x3o3o - capto)
- Klitizing, (x3o3x3x3x3o3o - capro)
- Klitizing, (o3x3x3o3x3x3o - bicpath)
- Klitizing, (x3x3x3x3x3o3o - gecco)
- Klitizing, (o3x3x3x3x3x3o - gabach)
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