6-orthoplex |
Stericated 6-orthoplex |
Steritruncated 6-orthoplex |
Stericantellated 6-orthoplex |
Stericantitruncated 6-orthoplex |
Steriruncinated 6-orthoplex |
Steriruncitruncated 6-orthoplex |
Steriruncicantellated 6-orthoplex |
Steriruncicantitruncated 6-orthoplex |
Orthogonal projections in B6 Coxeter plane |
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In six-dimensional geometry, a stericated 6-orthoplex is a convex uniform 6-polytope, constructed as a sterication (4th order truncation) of the regular 6-orthoplex.
There are 16 unique sterications for the 6-orthoplex with permutations of truncations, cantellations, and runcinations. Eight are better represented from the stericated 6-cube.
Stericated 6-orthoplex | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | 2r2r{3,3,3,3,4} |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 5760 |
Vertices | 960 |
Vertex figure | |
Coxeter groups | B6, [4,3,3,3,3] |
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] |
Steritruncated 6-orthoplex | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,1,4{3,3,3,3,4} |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 19200 |
Vertices | 3840 |
Vertex figure | |
Coxeter groups | B6, [4,3,3,3,3] |
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] |
Stericantellated 6-orthoplex | |
---|---|
Type | uniform 6-polytope |
Schläfli symbols | t0,2,4{34,4} rr2r{3,3,3,3,4} |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 28800 |
Vertices | 5760 |
Vertex figure | |
Coxeter groups | B6, [4,3,3,3,3] |
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] |
Stericantitruncated 6-orthoplex | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,1,2,4{3,3,3,3,4} |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 46080 |
Vertices | 11520 |
Vertex figure | |
Coxeter groups | B6, [4,3,3,3,3] |
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] |
Steriruncinated 6-orthoplex | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,3,4{3,3,3,3,4} |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 15360 |
Vertices | 3840 |
Vertex figure | |
Coxeter groups | B6, [4,3,3,3,3] |
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] |
Steriruncitruncated 6-orthoplex | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | 2t2r{3,3,3,3,4} |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 40320 |
Vertices | 11520 |
Vertex figure | |
Coxeter groups | B6, [4,3,3,3,3] |
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] |
Steriruncicantellated 6-orthoplex | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,2,3,4{3,3,3,3,4} |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 40320 |
Vertices | 11520 |
Vertex figure | |
Coxeter groups | B6, [4,3,3,3,3] |
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] |
Steriuncicantitruncated 6-orthoplex | |
---|---|
Type | uniform 6-polytope |
Schläfli symbols | t0,1,2,3,4{34,4} tr2r{3,3,3,3,4} |
Coxeter-Dynkin diagrams | |
5-faces | 536: 12 t0,1,2,3{3,3,3,4} 60 {}×t0,1,2{3,3,4} × 160 {6}×t0,1,2{3,3} × 240 {4}×t0,1,2{3,3} × 64 t0,1,2,3,4{34} |
4-faces | 8216 |
Cells | 38400 |
Faces | 76800 |
Edges | 69120 |
Vertices | 23040 |
Vertex figure | irregular 5-simplex |
Coxeter groups | B6, [4,3,3,3,3] |
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] |
The snub 6-demicube defined as an alternation of the omnitruncated 6-demicube is not uniform, but it can be given Coxeter diagram or and symmetry [32,1,1,1]+ or [4,(3,3,3,3)+], and constructed from 12 snub 5-demicubes, 64 snub 5-simplexes, 60 snub 24-cell antiprisms, 160 3-s{3,4} duoantiprisms, 240 2-sr{3,3} duoantiprisms, and 11520 irregular 5-simplexes filling the gaps at the deleted vertices.
These polytopes are from a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-orthoplex or 6-orthoplex.