Steric 6-cubes
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In six-dimensional geometry, a steric 6-cube is a convex uniform 6-polytope. There are unique 4 steric forms of the 6-cube.
![]() 6-demicube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Steric 6-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Stericantic 6-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Steriruncic 6-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Stericruncicantic 6-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
Orthogonal projections in D5 Coxeter plane |
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Steric 6-cube
Steric 6-cube | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,3{3,33,1} h4{4,34} |
Coxeter-Dynkin diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 3360 |
Vertices | 480 |
Vertex figure | |
Coxeter groups | D6, [33,1,1] |
Properties | convex |
Alternate names
- Runcinated demihexeract
- Runcinated 6-demicube
- Small prismated hemihexeract (Acronym: sophax) (Jonathan Bowers)[1]
Cartesian coordinates
The Cartesian coordinates for the 480 vertices of a steric 6-cube centered at the origin are coordinate permutations:
- (±1,±1,±1,±1,±1,±3)
with an odd number of plus signs.
Images
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] |
Related polytopes
Stericantic 6-cube
Stericantic 6-cube | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,1,3{3,33,1} h2,4{4,34} |
Coxeter-Dynkin diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 12960 |
Vertices | 2880 |
Vertex figure | |
Coxeter groups | D6, [33,1,1] |
Properties | convex |
Alternate names
- Runcitruncated demihexeract
- Runcitruncated 6-demicube
- Prismatotruncated hemihexeract (Acronym: pithax) (Jonathan Bowers)[2]
Cartesian coordinates
The Cartesian coordinates for the 2880 vertices of a stericantic 6-cube centered at the origin are coordinate permutations:
- (±1,±1,±1,±3,±3,±5)
with an odd number of plus signs.
Images
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] |
Steriruncic 6-cube
Steriruncic 6-cube | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,2,3{3,33,1} h3,4{4,34} |
Coxeter-Dynkin diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 7680 |
Vertices | 1920 |
Vertex figure | |
Coxeter groups | D6, [33,1,1] |
Properties | convex |
Alternate names
- Runcicantellated demihexeract
- Runcicantellated 6-demicube
- Prismatorhombated hemihexeract (Acronym: prohax) (Jonathan Bowers)[3]
Cartesian coordinates
The Cartesian coordinates for the 1920 vertices of a steriruncic 6-cube centered at the origin are coordinate permutations:
- (±1,±1,±1,±1,±3,±5)
with an odd number of plus signs.
Images
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] |
Steriruncicantic 6-cube
Steriruncicantic 6-cube | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,1,2,3{3,32,1} h2,3,4{4,34} |
Coxeter-Dynkin diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 17280 |
Vertices | 5760 |
Vertex figure | |
Coxeter groups | D6, [33,1,1] |
Properties | convex |
Alternate names
- Runcicantitruncated demihexeract
- Runcicantitruncated 6-demicube
- Great prismated hemihexeract (Acronym: gophax) (Jonathan Bowers)[4]
Cartesian coordinates
The Cartesian coordinates for the 5760 vertices of a steriruncicantic 6-cube centered at the origin are coordinate permutations:
- (±1,±1,±1,±3,±5,±7)
with an odd number of plus signs.
Images
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] |
Related polytopes
There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 are unique:
Notes
References
External links
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