Orthogonal projections in B6 Coxeter plane | ||
---|---|---|
7-orthoplex |
Stericated 7-orthoplex |
Steritruncated 7-orthoplex |
Bisteritruncated 7-orthoplex |
Stericantellated 7-orthoplex |
Stericantitruncated 7-orthoplex |
Bistericantitruncated 7-orthoplex |
Steriruncinated 7-orthoplex |
Steriruncitruncated 7-orthoplex |
Steriruncicantellated 7-orthoplex |
Bisteriruncitruncated 7-orthoplex |
Steriruncicantitruncated 7-orthoplex |
In seven-dimensional geometry, a stericated 7-orthoplex is a convex uniform 7-polytope with 4th order truncations ( sterication) of the regular 7-orthoplex.
There are 24 unique sterication for the 7-orthoplex with permutations of truncations, cantellations, and runcinations. 14 are more simply constructed from the 7-cube.
This polytope is one of 127 uniform 7-polytopes with B7 symmetry.
Stericated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
steritruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
bisteritruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1,2,5{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Stericantellated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,2,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
stericantitruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
bistericantitruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1,2,3,5{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Steriruncinated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,3,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | too complex | ||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
steriruncitruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,3,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
steriruncicantellated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,2,3,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
steriruncicantitruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,3,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Orthogonal projections in B6 Coxeter plane | ||
---|---|---|
7-orthoplex |
Stericated 7-orthoplex |
Steritruncated 7-orthoplex |
Bisteritruncated 7-orthoplex |
Stericantellated 7-orthoplex |
Stericantitruncated 7-orthoplex |
Bistericantitruncated 7-orthoplex |
Steriruncinated 7-orthoplex |
Steriruncitruncated 7-orthoplex |
Steriruncicantellated 7-orthoplex |
Bisteriruncitruncated 7-orthoplex |
Steriruncicantitruncated 7-orthoplex |
In seven-dimensional geometry, a stericated 7-orthoplex is a convex uniform 7-polytope with 4th order truncations ( sterication) of the regular 7-orthoplex.
There are 24 unique sterication for the 7-orthoplex with permutations of truncations, cantellations, and runcinations. 14 are more simply constructed from the 7-cube.
This polytope is one of 127 uniform 7-polytopes with B7 symmetry.
Stericated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
steritruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
bisteritruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1,2,5{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Stericantellated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,2,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
stericantitruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
bistericantitruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1,2,3,5{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Steriruncinated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,3,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | too complex | ||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
steriruncitruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,3,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
steriruncicantellated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,2,3,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
steriruncicantitruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,3,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |