Stericated 7-simplexes
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In seven-dimensional geometry, a stericated 7-simplex is a convex uniform 7-polytope with 4th order truncations (sterication) of the regular 7-simplex.
![]() 7-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Stericated 7-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bistericated 7-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Steritruncated 7-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bisteritruncated 7-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Stericantellated 7-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bistericantellated 7-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Stericantitruncated 7-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bistericantitruncated 7-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Steriruncinated 7-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Steriruncitruncated 7-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Steriruncicantellated 7-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bisteriruncitruncated 7-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Steriruncicantitruncated 7-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bisteriruncicantitruncated 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 | uniform 7-polytope |
Schläfli symbol | t0,4{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 2240 |
Vertices | 280 |
Vertex figure | |
Coxeter group | A7, [36], order 40320 |
Properties | convex |
Alternate names
- Small cellated octaexon (acronym: sco) (Jonathan Bowers)[1]
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
Ak Coxeter plane | A7 | A6 | A5 |
---|---|---|---|
Graph | ![]() |
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Dihedral symmetry | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 |
Graph | ![]() |
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Dihedral symmetry | [5] | [4] | [3] |
Bistericated 7-simplex
bistericated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1,5{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 3360 |
Vertices | 420 |
Vertex figure | |
Coxeter group | A7×2, [[36]], order 80320 |
Properties | convex |
Alternate names
- Small bicellated hexadecaexon (acronym: sabach) (Jonathan Bowers)[2]
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
Ak Coxeter plane | A7 | A6 | A5 |
---|---|---|---|
Graph | ![]() |
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Dihedral symmetry | [8] | [[7]] | [6] |
Ak Coxeter plane | A4 | A3 | A2 |
Graph | ![]() |
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Dihedral symmetry | [[5]] | [4] | [[3]] |
Steritruncated 7-simplex
steritruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,4{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 7280 |
Vertices | 1120 |
Vertex figure | |
Coxeter group | A7, [36], order 40320 |
Properties | convex |
Alternate names
- Cellitruncated octaexon (acronym: cato) (Jonathan Bowers)[3]
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
Ak Coxeter plane | A7 | A6 | A5 |
---|---|---|---|
Graph | ![]() |
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Dihedral symmetry | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 |
Graph | ![]() |
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Dihedral symmetry | [5] | [4] | [3] |
Bisteritruncated 7-simplex
bisteritruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1,2,5{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 9240 |
Vertices | 1680 |
Vertex figure | |
Coxeter group | A7, [36], order 40320 |
Properties | convex |
Alternate names
- Bicellitruncated octaexon (acronym: bacto) (Jonathan Bowers)[4]
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
Ak Coxeter plane | A7 | A6 | A5 |
---|---|---|---|
Graph | ![]() |
![]() |
![]() |
Dihedral symmetry | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 |
Graph | ![]() |
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Dihedral symmetry | [5] | [4] | [3] |
Stericantellated 7-simplex
Stericantellated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,2,4{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 10080 |
Vertices | 1680 |
Vertex figure | |
Coxeter group | A7, [36], order 40320 |
Properties | convex |
Alternate names
- Cellirhombated octaexon (acronym: caro) (Jonathan Bowers)[5]
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
Ak Coxeter plane | A7 | A6 | A5 |
---|---|---|---|
Graph | ![]() |
![]() |
![]() |
Dihedral symmetry | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 |
Graph | ![]() |
![]() |
![]() |
Dihedral symmetry | [5] | [4] | [3] |
Bistericantellated 7-simplex
Bistericantellated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1,3,5{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 15120 |
Vertices | 2520 |
Vertex figure | |
Coxeter group | A7×2, [[36]], order 80320 |
Properties | convex |
Alternate names
- Bicellirhombihexadecaexon (acronym: bacroh) (Jonathan Bowers)[6]
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
Ak Coxeter plane | A7 | A6 | A5 |
---|---|---|---|
Graph | ![]() |
![]() |
![]() |
Dihedral symmetry | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 |
Graph | ![]() |
![]() |
![]() |
Dihedral symmetry | [5] | [4] | [3] |
Stericantitruncated 7-simplex
stericantitruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,4{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 16800 |
Vertices | 3360 |
Vertex figure | |
Coxeter group | A7, [36], order 40320 |
Properties | convex |
Alternate names
- Celligreatorhombated octaexon (acronym: cagro) (Jonathan Bowers)[7]
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
Ak Coxeter plane | A7 | A6 | A5 |
---|---|---|---|
Graph | ![]() |
![]() |
![]() |
Dihedral symmetry | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 |
Graph | ![]() |
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Dihedral symmetry | [5] | [4] | [3] |
Bistericantitruncated 7-simplex
bistericantitruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1,2,3,5{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 22680 |
Vertices | 5040 |
Vertex figure | |
Coxeter group | A7, [36], order 40320 |
Properties | convex |
Alternate names
- Bicelligreatorhombated octaexon (acronym: bacogro) (Jonathan Bowers)[8]
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
Ak Coxeter plane | A7 | A6 | A5 |
---|---|---|---|
Graph | ![]() |
![]() |
![]() |
Dihedral symmetry | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 |
Graph | ![]() |
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Dihedral symmetry | [5] | [4] | [3] |
Steriruncinated 7-simplex
Steriruncinated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,3,4{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 5040 |
Vertices | 1120 |
Vertex figure | |
Coxeter group | A7, [36], order 40320 |
Properties | convex |
Alternate names
- Celliprismated octaexon (acronym: cepo) (Jonathan Bowers)[9]
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
Ak Coxeter plane | A7 | A6 | A5 |
---|---|---|---|
Graph | ![]() |
![]() |
![]() |
Dihedral symmetry | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 |
Graph | ![]() |
![]() |
![]() |
Dihedral symmetry | [5] | [4] | [3] |
Steriruncitruncated 7-simplex
steriruncitruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,3,4{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 13440 |
Vertices | 3360 |
Vertex figure | |
Coxeter group | A7, [36], order 40320 |
Properties | convex |
Alternate names
- Celliprismatotruncated octaexon (acronym: capto) (Jonathan Bowers)[10]
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
Ak Coxeter plane | A7 | A6 | A5 |
---|---|---|---|
Graph | ![]() |
![]() |
![]() |
Dihedral symmetry | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 |
Graph | ![]() |
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Dihedral symmetry | [5] | [4] | [3] |
Steriruncicantellated 7-simplex
steriruncicantellated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,2,3,4{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 13440 |
Vertices | 3360 |
Vertex figure | |
Coxeter group | A7, [36], order 40320 |
Properties | convex |
Alternate names
- Celliprismatorhombated octaexon (acronym: capro) (Jonathan Bowers)[11]
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
Ak Coxeter plane | A7 | A6 | A5 |
---|---|---|---|
Graph | ![]() |
![]() |
![]() |
Dihedral symmetry | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 |
Graph | ![]() |
![]() |
![]() |
Dihedral symmetry | [5] | [4] | [3] |
Bisteriruncitruncated 7-simplex
bisteriruncitruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1,2,4,5{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 20160 |
Vertices | 5040 |
Vertex figure | |
Coxeter group | A7×2, [[36]], order 80320 |
Properties | convex |
Alternate names
- Bicelliprismatotruncated hexadecaexon (acronym: bicpath) (Jonathan Bowers)[12]
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
Ak Coxeter plane | A7 | A6 | A5 |
---|---|---|---|
Graph | ![]() |
![]() |
![]() |
Dihedral symmetry | [8] | [[7]] | [6] |
Ak Coxeter plane | A4 | A3 | A2 |
Graph | ![]() |
![]() |
![]() |
Dihedral symmetry | [[5]] | [4] | [[3]] |
Steriruncicantitruncated 7-simplex
steriruncicantitruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,3,4{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 23520 |
Vertices | 6720 |
Vertex figure | |
Coxeter group | A7, [36], order 40320 |
Properties | convex |
Alternate names
- Great cellated octaexon (acronym: gecco) (Jonathan Bowers)[13]
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
Ak Coxeter plane | A7 | A6 | A5 |
---|---|---|---|
Graph | ![]() |
![]() |
![]() |
Dihedral symmetry | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 |
Graph | ![]() |
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Dihedral symmetry | [5] | [4] | [3] |
Bisteriruncicantitruncated 7-simplex
bisteriruncicantitruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1,2,3,4,5{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 35280 |
Vertices | 10080 |
Vertex figure | |
Coxeter group | A7×2, [[36]], order 80320 |
Properties | convex |
Alternate names
- Great bicellated hexadecaexon (gabach) (Jonathan Bowers) [14]
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
Ak Coxeter plane | A7 | A6 | A5 |
---|---|---|---|
Graph | ![]() |
![]() |
![]() |
Dihedral symmetry | [8] | [[7]] | [6] |
Ak Coxeter plane | A4 | A3 | A2 |
Graph | ![]() |
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Dihedral symmetry | [[5]] | [4] | [[3]] |
Related polytopes
This polytope is one of 71 uniform 7-polytopes with A7 symmetry.
Notes
References
External links
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