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In six-dimensional geometry, a pentic 6-cube is a convex uniform 6-polytope.
6-demicube (half 6-cube) = |
Pentic 6-cube = |
Penticantic 6-cube = |
Pentiruncic 6-cube = |
Pentiruncicantic 6-cube = |
Pentisteric 6-cube = |
Pentistericantic 6-cube = |
Pentisteriruncic 6-cube = |
Pentisteriruncicantic 6-cube = |
Orthogonal projections in D6 Coxeter plane |
---|
There are 8 pentic forms of the 6-cube.
Pentic 6-cube | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,4{3,34,1} h5{4,34} |
Coxeter-Dynkin diagram | = |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 1440 |
Vertices | 192 |
Vertex figure | |
Coxeter groups | D6, [33,1,1] |
Properties | convex |
The pentic 6-cube, , has half of the vertices of a pentellated 6-cube, .
The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane | B6 | |
---|---|---|
Graph | ||
Dihedral symmetry | [12/2] | |
Coxeter plane | D6 | D5 |
Graph | ||
Dihedral symmetry | [10] | [8] |
Coxeter plane | D4 | D3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Coxeter plane | A5 | A3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Penticantic 6-cube | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,1,4{3,34,1} h2,5{4,34} |
Coxeter-Dynkin diagram | = |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 9600 |
Vertices | 1920 |
Vertex figure | |
Coxeter groups | D6, [33,1,1] |
Properties | convex |
The penticantic 6-cube, , has half of the vertices of a penticantellated 6-cube, .
The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane | B6 | |
---|---|---|
Graph | ||
Dihedral symmetry | [12/2] | |
Coxeter plane | D6 | D5 |
Graph | ||
Dihedral symmetry | [10] | [8] |
Coxeter plane | D4 | D3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Coxeter plane | A5 | A3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Pentiruncic 6-cube | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,2,4{3,34,1} h3,5{4,34} |
Coxeter-Dynkin diagram | = |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 10560 |
Vertices | 1920 |
Vertex figure | |
Coxeter groups | D6, [33,1,1] |
Properties | convex |
The pentiruncic 6-cube, , has half of the vertices of a pentiruncinated 6-cube (penticantellated 6-orthoplex), .
The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane | B6 | |
---|---|---|
Graph | ||
Dihedral symmetry | [12/2] | |
Coxeter plane | D6 | D5 |
Graph | ||
Dihedral symmetry | [10] | [8] |
Coxeter plane | D4 | D3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Coxeter plane | A5 | A3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Pentiruncicantic 6-cube | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,1,2,4{3,32,1} h2,3,5{4,34} |
Coxeter-Dynkin diagram | = |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 20160 |
Vertices | 5760 |
Vertex figure | |
Coxeter groups | D6, [33,1,1] |
Properties | convex |
The pentiruncicantic 6-cube, , has half of the vertices of a pentiruncicantellated 6-cube or (pentiruncicantellated 6-orthoplex),
The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane | B6 | |
---|---|---|
Graph | ||
Dihedral symmetry | [12/2] | |
Coxeter plane | D6 | D5 |
Graph | ||
Dihedral symmetry | [10] | [8] |
Coxeter plane | D4 | D3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Coxeter plane | A5 | A3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Pentisteric 6-cube | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,3,4{3,34,1} h4,5{4,34} |
Coxeter-Dynkin diagram | = |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 5280 |
Vertices | 960 |
Vertex figure | |
Coxeter groups | D6, [33,1,1] |
Properties | convex |
The pentisteric 6-cube, , has half of the vertices of a pentistericated 6-cube (pentitruncated 6-orthoplex),
The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane | B6 | |
---|---|---|
Graph | ||
Dihedral symmetry | [12/2] | |
Coxeter plane | D6 | D5 |
Graph | ||
Dihedral symmetry | [10] | [8] |
Coxeter plane | D4 | D3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Coxeter plane | A5 | A3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Pentistericantic 6-cube | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,1,3,4{3,34,1} h2,4,5{4,34} |
Coxeter-Dynkin diagram | = |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 23040 |
Vertices | 5760 |
Vertex figure | |
Coxeter groups | D6, [33,1,1] |
Properties | convex |
The pentistericantic 6-cube, , has half of the vertices of a pentistericantellated 6-cube (pentiruncitruncated 6-orthoplex), .
The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane | B6 | |
---|---|---|
Graph | ||
Dihedral symmetry | [12/2] | |
Coxeter plane | D6 | D5 |
Graph | ||
Dihedral symmetry | [10] | [8] |
Coxeter plane | D4 | D3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Coxeter plane | A5 | A3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Pentisteriruncic 6-cube | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,2,3,4{3,34,1} h3,4,5{4,34} |
Coxeter-Dynkin diagram | = |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 15360 |
Vertices | 3840 |
Vertex figure | |
Coxeter groups | D6, [33,1,1] |
Properties | convex |
The pentisteriruncic 6-cube, , has half of the vertices of a pentisteriruncinated 6-cube (penticantitruncated 6-orthoplex), .
The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane | B6 | |
---|---|---|
Graph | ||
Dihedral symmetry | [12/2] | |
Coxeter plane | D6 | D5 |
Graph | ||
Dihedral symmetry | [10] | [8] |
Coxeter plane | D4 | D3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Coxeter plane | A5 | A3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Pentisteriruncicantic 6-cube | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,1,2,3,4{3,32,1} h2,3,4,5{4,34} |
Coxeter-Dynkin diagram | = |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 34560 |
Vertices | 11520 |
Vertex figure | |
Coxeter groups | D6, [33,1,1] |
Properties | convex |
The pentisteriruncicantic 6-cube, , has half of the vertices of a pentisteriruncicantellated 6-cube (pentisteriruncicantitruncated 6-orthoplex), .
The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane | B6 | |
---|---|---|
Graph | ||
Dihedral symmetry | [12/2] | |
Coxeter plane | D6 | D5 |
Graph | ||
Dihedral symmetry | [10] | [8] |
Coxeter plane | D4 | D3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Coxeter plane | A5 | A3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 are unique:
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