![]() 7-orthoplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Truncated 7-orthoplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bitruncated 7-orthoplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Tritruncated 7-orthoplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Truncated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bitruncated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Tritruncated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Orthogonal projections in B7 Coxeter plane |
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In seven-dimensional geometry, a truncated 7-orthoplex is a convex uniform 7-polytope, being a truncation of the regular 7-orthoplex.
There are 6 truncations of the 7-orthoplex. Vertices of the truncation 7-orthoplex are located as pairs on the edge of the 7-orthoplex. Vertices of the bitruncated 7-orthoplex are located on the triangular faces of the 7-orthoplex. Vertices of the tritruncated 7-orthoplex are located inside the tetrahedral cells of the 7-orthoplex. The final three truncations are best expressed relative to the 7-cube.
Truncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t{35,4} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]()
|
6-faces | |
5-faces | |
4-faces | |
Cells | 3920 |
Faces | 2520 |
Edges | 924 |
Vertices | 168 |
Vertex figure | ( )v{3,3,4} |
Coxeter groups | B7, [35,4] D7, [34,1,1] |
Properties | convex |
Cartesian coordinates for the vertices of a truncated 7-orthoplex, centered at the origin, are all 168 vertices are sign (4) and coordinate (42) permutations of
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph |
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Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph |
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Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph |
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Dihedral symmetry | [6] | [4] |
There are two Coxeter groups associated with the truncated 7-orthoplex, one with the C7 or [4,35] Coxeter group, and a lower symmetry with the D7 or [34,1,1] Coxeter group.
Bitruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | 2t{35,4} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]()
|
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 4200 |
Vertices | 840 |
Vertex figure | { }v{3,3,4} |
Coxeter groups | B7, [35,4] D7, [34,1,1] |
Properties | convex |
Cartesian coordinates for the vertices of a bitruncated 7-orthoplex, centered at the origin, are all sign and coordinate permutations of
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph |
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Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph |
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Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph |
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Dihedral symmetry | [6] | [4] |
The tritruncated 7-orthoplex can tessellation space in the quadritruncated 7-cubic honeycomb.
Tritruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | 3t{35,4} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]()
|
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 10080 |
Vertices | 2240 |
Vertex figure | {3}v{3,4} |
Coxeter groups | B7, [35,4] D7, [34,1,1] |
Properties | convex |
Cartesian coordinates for the vertices of a tritruncated 7-orthoplex, centered at the origin, are all sign and coordinate permutations of
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph |
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Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph |
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Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph |
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Dihedral symmetry | [6] | [4] |
![]() 7-orthoplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Truncated 7-orthoplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bitruncated 7-orthoplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Tritruncated 7-orthoplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Truncated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bitruncated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Tritruncated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Orthogonal projections in B7 Coxeter plane |
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In seven-dimensional geometry, a truncated 7-orthoplex is a convex uniform 7-polytope, being a truncation of the regular 7-orthoplex.
There are 6 truncations of the 7-orthoplex. Vertices of the truncation 7-orthoplex are located as pairs on the edge of the 7-orthoplex. Vertices of the bitruncated 7-orthoplex are located on the triangular faces of the 7-orthoplex. Vertices of the tritruncated 7-orthoplex are located inside the tetrahedral cells of the 7-orthoplex. The final three truncations are best expressed relative to the 7-cube.
Truncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t{35,4} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]()
|
6-faces | |
5-faces | |
4-faces | |
Cells | 3920 |
Faces | 2520 |
Edges | 924 |
Vertices | 168 |
Vertex figure | ( )v{3,3,4} |
Coxeter groups | B7, [35,4] D7, [34,1,1] |
Properties | convex |
Cartesian coordinates for the vertices of a truncated 7-orthoplex, centered at the origin, are all 168 vertices are sign (4) and coordinate (42) permutations of
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 |
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Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph |
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Dihedral symmetry | [6] | [4] |
There are two Coxeter groups associated with the truncated 7-orthoplex, one with the C7 or [4,35] Coxeter group, and a lower symmetry with the D7 or [34,1,1] Coxeter group.
Bitruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | 2t{35,4} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]()
|
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 4200 |
Vertices | 840 |
Vertex figure | { }v{3,3,4} |
Coxeter groups | B7, [35,4] D7, [34,1,1] |
Properties | convex |
Cartesian coordinates for the vertices of a bitruncated 7-orthoplex, centered at the origin, are all sign and coordinate permutations of
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph |
![]() |
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Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph |
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Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph |
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Dihedral symmetry | [6] | [4] |
The tritruncated 7-orthoplex can tessellation space in the quadritruncated 7-cubic honeycomb.
Tritruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | 3t{35,4} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]()
|
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 10080 |
Vertices | 2240 |
Vertex figure | {3}v{3,4} |
Coxeter groups | B7, [35,4] D7, [34,1,1] |
Properties | convex |
Cartesian coordinates for the vertices of a tritruncated 7-orthoplex, centered at the origin, are all sign and coordinate permutations of
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 |
![]() |
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Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph |
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Dihedral symmetry | [6] | [4] |