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In seven-dimensional geometry, a runcinated 7-cube is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-cube.
![]() 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Runcinated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Biruncinated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Runcitruncated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Biruncitruncated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Runcicantellated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Biruncicantellated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Runcicantitruncated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Biruncicantitruncated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Orthogonal projections in B7 Coxeter plane |
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There are 16 unique runcinations of the 7-cube with permutations of truncations, and cantellations. 8 are more simply constructed from the 7-orthoplex.
These polytopes are among 127 uniform 7-polytopes with B7 symmetry.
Runcinated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,3{4,35} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 33600 |
Vertices | 4480 |
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] |
Biruncinated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1,4{4,35} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 67200 |
Vertices | 8960 |
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] |
Runcitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,3{4,35} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 73920 |
Vertices | 13440 |
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] |
Biruncitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1,2,4{4,35} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 134400 |
Vertices | 26880 |
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] |
Runcicantellated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,2,3{4,35} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 53760 |
Vertices | 13440 |
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] |
biruncicantellated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1,3,4{4,35} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 120960 |
Vertices | 26880 |
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] |
Runcicantitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,3{4,35} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 94080 |
Vertices | 26880 |
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] |
biruncicantitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1,2,3,4{4,35} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 188160 |
Vertices | 53760 |
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] |
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