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In six-dimensional geometry, a truncated 6-orthoplex is a convex uniform 6-polytope, being a truncation of the regular 6-orthoplex.
![]() 6-orthoplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Truncated 6-orthoplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bitruncated 6-orthoplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Tritruncated 6-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() 6-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Truncated 6-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bitruncated 6-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
Orthogonal projections in B6 Coxeter plane |
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There are 5 degrees of truncation for the 6-orthoplex. Vertices of the truncated 6-orthoplex are located as pairs on the edge of the 6-orthoplex. Vertices of the bitruncated 6-orthoplex are located on the triangular faces of the 6-orthoplex. Vertices of the tritruncated 6-orthoplex are located inside the tetrahedral cells of the 6-orthoplex.
Truncated 6-orthoplex | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t{3,3,3,3,4} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5-faces | 76 |
4-faces | 576 |
Cells | 1200 |
Faces | 1120 |
Edges | 540 |
Vertices | 120 |
Vertex figure | ![]() ( )v{3,4} |
Coxeter groups | B6, [3,3,3,3,4] D6, [33,1,1] |
Properties | convex |
There are two Coxeter groups associated with the truncated hexacross, one with the C6 or [4,3,3,3,3] Coxeter group, and a lower symmetry with the D6 or [33,1,1] Coxeter group.
Cartesian coordinates for the vertices of a truncated 6-orthoplex, centered at the origin, are all 120 vertices are sign (4) and coordinate (30) permutations of
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | ![]() |
![]() |
![]() |
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | ![]() |
![]() | |
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | ![]() |
![]() | |
Dihedral symmetry | [6] | [4] |
Bitruncated 6-orthoplex | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | 2t{3,3,3,3,4} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | ![]() { }v{3,4} |
Coxeter groups | B6, [3,3,3,3,4] D6, [33,1,1] |
Properties | convex |
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | ![]() |
![]() |
![]() |
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | ![]() |
![]() | |
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | ![]() |
![]() | |
Dihedral symmetry | [6] | [4] |
These polytopes are a part of a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.
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