7-simplex |
Pentellated 7-simplex |
Pentitruncated 7-simplex |
Penticantellated 7-simplex |
Penticantitruncated 7-simplex |
Pentiruncinated 7-simplex |
Pentiruncitruncated 7-simplex |
Pentiruncicantellated 7-simplex |
Pentiruncicantitruncated 7-simplex |
Pentistericated 7-simplex |
Pentisteritruncated 7-simplex |
Pentistericantellated 7-simplex |
Pentistericantitruncated 7-simplex |
Pentisteriruncinated 7-simplex |
Pentisteriruncitruncated 7-simplex |
Pentisteriruncicantellated 7-simplex |
Pentisteriruncicantitruncated 7-simplex |
In seven-dimensional geometry, a pentellated 7-simplex is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-simplex.
There are 16 unique pentellations of the 7-simplex with permutations of truncations, cantellations, runcinations, and sterications.
Pentellated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,5}{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 1260 |
Vertices | 168 |
Vertex figure | |
Coxeter groups | A_{7}, [3,3,3,3,3,3] |
Properties | convex |
The vertices of the pentellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,1,1,1,2). This construction is based on facets of the pentellated 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] |
pentitruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,1,5}{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 5460 |
Vertices | 840 |
Vertex figure | |
Coxeter groups | A_{7}, [3,3,3,3,3,3] |
Properties | convex |
The vertices of the pentitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,1,1,2,3). This construction is based on facets of the pentitruncated 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] |
Penticantellated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,2,5}{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 11760 |
Vertices | 1680 |
Vertex figure | |
Coxeter groups | A_{7}, [3,3,3,3,3,3] |
Properties | convex |
The vertices of the penticantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,1,2,2,3). This construction is based on facets of the penticantellated 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] |
penticantitruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,1,2,5}{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | A_{7}, [3,3,3,3,3,3] |
Properties | convex |
The vertices of the penticantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,1,2,3,4). This construction is based on facets of the penticantitruncated 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] |
pentiruncinated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,3,5}{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 10920 |
Vertices | 1680 |
Vertex figure | |
Coxeter groups | A_{7}, [3,3,3,3,3,3] |
Properties | convex |
The vertices of the pentiruncinated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,2,2,2,3). This construction is based on facets of the pentiruncinated 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] |
pentiruncitruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,1,3,5}{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 27720 |
Vertices | 5040 |
Vertex figure | |
Coxeter groups | A_{7}, [3,3,3,3,3,3] |
Properties | convex |
The vertices of the pentiruncitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,2,2,3,4). This construction is based on facets of the pentiruncitruncated 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] |
pentiruncicantellated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,2,3,5}{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 25200 |
Vertices | 5040 |
Vertex figure | |
Coxeter groups | A_{7}, [3,3,3,3,3,3] |
Properties | convex |
The vertices of the pentiruncicantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,2,3,3,4). This construction is based on facets of the pentiruncicantellated 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] |
pentiruncicantitruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,1,2,3,5}{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 45360 |
Vertices | 10080 |
Vertex figure | |
Coxeter groups | A_{7}, [3,3,3,3,3,3] |
Properties | convex |
The vertices of the pentiruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,2,3,4,5). This construction is based on facets of the pentiruncicantitruncated 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] |
pentistericated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,4,5}{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 4200 |
Vertices | 840 |
Vertex figure | |
Coxeter groups | A_{7}, [3,3,3,3,3,3] |
Properties | convex |
The vertices of the pentistericated 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 pentistericated 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] |
pentisteritruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,1,4,5}{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 15120 |
Vertices | 3360 |
Vertex figure | |
Coxeter groups | A_{7}, [3,3,3,3,3,3] |
Properties | convex |
The vertices of the pentisteritruncated 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 pentisteritruncated 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] |
pentistericantellated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,2,4,5}{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 25200 |
Vertices | 5040 |
Vertex figure | |
Coxeter groups | A_{7}, [3,3,3,3,3,3] |
Properties | convex |
The vertices of the pentistericantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,2,2,3,3,4). This construction is based on facets of the pentistericantellated 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] |
pentistericantitruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,1,2,4,5}{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 40320 |
Vertices | 10080 |
Vertex figure | |
Coxeter groups | A_{7}, [3,3,3,3,3,3] |
Properties | convex |
The vertices of the pentistericantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,2,2,3,4,5). This construction is based on facets of the pentistericantitruncated 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] |
Pentisteriruncinated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,3,4,5}{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 15120 |
Vertices | 3360 |
Vertex figure | |
Coxeter groups | A_{7}, [3,3,3,3,3,3] |
Properties | convex |
The vertices of the pentisteriruncinated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,2,3,3,3,4). This construction is based on facets of the pentisteriruncinated 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] |
pentisteriruncitruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,1,3,4,5}{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 40320 |
Vertices | 10080 |
Vertex figure | |
Coxeter groups | A_{7}, [3,3,3,3,3,3] |
Properties | convex |
The vertices of the pentisteriruncitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,2,3,3,4,5). This construction is based on facets of the pentisteriruncitruncated 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]] |
pentisteriruncicantellated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,2,3,4,5}{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 40320 |
Vertices | 10080 |
Vertex figure | |
Coxeter groups | A_{7}, [3,3,3,3,3,3] |
Properties | convex |
The vertices of the pentisteriruncicantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,2,3,4,4,5). This construction is based on facets of the pentisteriruncicantellated 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]] |
pentisteriruncicantitruncated 7-simplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t_{0,1,2,3,4,5}{3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 70560 |
Vertices | 20160 |
Vertex figure | |
Coxeter groups | A_{7}, [3,3,3,3,3,3] |
Properties | convex |
The vertices of the pentisteriruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,2,3,4,5,6). This construction is based on facets of the pentisteriruncicantitruncated 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]] |
These polytopes are a part of a set of 71 uniform 7-polytopes with A_{7} symmetry.