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 |
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 | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,4}{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 | A_{7}, [3^{6}], order 40320 |
Properties | convex |
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.
A_{k} Coxeter plane | A_{7} | A_{6} | A_{5} |
---|---|---|---|
Graph | |||
Dihedral symmetry | [8] | [7] | [6] |
A_{k} Coxeter plane | A_{4} | A_{3} | A_{2} |
Graph | |||
Dihedral symmetry | [5] | [4] | [3] |
bistericated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{1,5}{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 | A_{7}×2, [[3^{6}]], order 80320 |
Properties | convex |
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.
A_{k} Coxeter plane | A_{7} | A_{6} | A_{5} |
---|---|---|---|
Graph | |||
Dihedral symmetry | [8] | [[7]] | [6] |
A_{k} Coxeter plane | A_{4} | A_{3} | A_{2} |
Graph | |||
Dihedral symmetry | [[5]] | [4] | [[3]] |
steritruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,1,4}{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 | A_{7}, [3^{6}], order 40320 |
Properties | convex |
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.
A_{k} Coxeter plane | A_{7} | A_{6} | A_{5} |
---|---|---|---|
Graph | |||
Dihedral symmetry | [8] | [7] | [6] |
A_{k} Coxeter plane | A_{4} | A_{3} | A_{2} |
Graph | |||
Dihedral symmetry | [5] | [4] | [3] |
bisteritruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{1,2,5}{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 | A_{7}, [3^{6}], order 40320 |
Properties | convex |
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.
A_{k} Coxeter plane | A_{7} | A_{6} | A_{5} |
---|---|---|---|
Graph | |||
Dihedral symmetry | [8] | [7] | [6] |
A_{k} Coxeter plane | A_{4} | A_{3} | A_{2} |
Graph | |||
Dihedral symmetry | [5] | [4] | [3] |
Stericantellated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,2,4}{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 | A_{7}, [3^{6}], order 40320 |
Properties | convex |
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.
A_{k} Coxeter plane | A_{7} | A_{6} | A_{5} |
---|---|---|---|
Graph | |||
Dihedral symmetry | [8] | [7] | [6] |
A_{k} Coxeter plane | A_{4} | A_{3} | A_{2} |
Graph | |||
Dihedral symmetry | [5] | [4] | [3] |
Bistericantellated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{1,3,5}{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 | A_{7}×2, [[3^{6}]], order 80320 |
Properties | convex |
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.
A_{k} Coxeter plane | A_{7} | A_{6} | A_{5} |
---|---|---|---|
Graph | |||
Dihedral symmetry | [8] | [7] | [6] |
A_{k} Coxeter plane | A_{4} | A_{3} | A_{2} |
Graph | |||
Dihedral symmetry | [5] | [4] | [3] |
stericantitruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,1,2,4}{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 | A_{7}, [3^{6}], order 40320 |
Properties | convex |
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.
A_{k} Coxeter plane | A_{7} | A_{6} | A_{5} |
---|---|---|---|
Graph | |||
Dihedral symmetry | [8] | [7] | [6] |
A_{k} Coxeter plane | A_{4} | A_{3} | A_{2} |
Graph | |||
Dihedral symmetry | [5] | [4] | [3] |
bistericantitruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{1,2,3,5}{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 | A_{7}, [3^{6}], order 40320 |
Properties | convex |
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.
A_{k} Coxeter plane | A_{7} | A_{6} | A_{5} |
---|---|---|---|
Graph | |||
Dihedral symmetry | [8] | [7] | [6] |
A_{k} Coxeter plane | A_{4} | A_{3} | A_{2} |
Graph | |||
Dihedral symmetry | [5] | [4] | [3] |
Steriruncinated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,3,4}{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 | A_{7}, [3^{6}], order 40320 |
Properties | convex |
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.
A_{k} Coxeter plane | A_{7} | A_{6} | A_{5} |
---|---|---|---|
Graph | |||
Dihedral symmetry | [8] | [7] | [6] |
A_{k} Coxeter plane | A_{4} | A_{3} | A_{2} |
Graph | |||
Dihedral symmetry | [5] | [4] | [3] |
steriruncitruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,1,3,4}{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 | A_{7}, [3^{6}], order 40320 |
Properties | convex |
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.
A_{k} Coxeter plane | A_{7} | A_{6} | A_{5} |
---|---|---|---|
Graph | |||
Dihedral symmetry | [8] | [7] | [6] |
A_{k} Coxeter plane | A_{4} | A_{3} | A_{2} |
Graph | |||
Dihedral symmetry | [5] | [4] | [3] |
steriruncicantellated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,2,3,4}{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 | A_{7}, [3^{6}], order 40320 |
Properties | convex |
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.
A_{k} Coxeter plane | A_{7} | A_{6} | A_{5} |
---|---|---|---|
Graph | |||
Dihedral symmetry | [8] | [7] | [6] |
A_{k} Coxeter plane | A_{4} | A_{3} | A_{2} |
Graph | |||
Dihedral symmetry | [5] | [4] | [3] |
bisteriruncitruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{1,2,4,5}{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 | A_{7}×2, [[3^{6}]], order 80320 |
Properties | convex |
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.
A_{k} Coxeter plane | A_{7} | A_{6} | A_{5} |
---|---|---|---|
Graph | |||
Dihedral symmetry | [8] | [[7]] | [6] |
A_{k} Coxeter plane | A_{4} | A_{3} | A_{2} |
Graph | |||
Dihedral symmetry | [[5]] | [4] | [[3]] |
steriruncicantitruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,1,2,3,4}{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 | A_{7}, [3^{6}], order 40320 |
Properties | convex |
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.
A_{k} Coxeter plane | A_{7} | A_{6} | A_{5} |
---|---|---|---|
Graph | |||
Dihedral symmetry | [8] | [7] | [6] |
A_{k} Coxeter plane | A_{4} | A_{3} | A_{2} |
Graph | |||
Dihedral symmetry | [5] | [4] | [3] |
bisteriruncicantitruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{1,2,3,4,5}{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 | A_{7}×2, [[3^{6}]], order 80320 |
Properties | convex |
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.
A_{k} Coxeter plane | A_{7} | A_{6} | A_{5} |
---|---|---|---|
Graph | |||
Dihedral symmetry | [8] | [[7]] | [6] |
A_{k} Coxeter plane | A_{4} | A_{3} | A_{2} |
Graph | |||
Dihedral symmetry | [[5]] | [4] | [[3]] |
This polytope is one of 71 uniform 7-polytopes with A_{7} symmetry.