Runcic 6-cubes
From Wikipedia, the free encyclopedia
In six-dimensional geometry, a runcic 6-cube is a convex uniform 6-polytope. There are 2 unique runcic for the 6-cube.
6-demicube |
Runcic 6-cube |
Runcicantic 6-cube | |
| Orthogonal projections in D6 Coxeter plane | |||
|---|---|---|---|
Runcic 6-cube
| Runcic 6-cube | |
|---|---|
| Type | uniform 6-polytope |
| Schläfli symbol | t0,2{3,33,1} h3{4,34} |
| Coxeter-Dynkin diagram | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 3840 |
| Vertices | 640 |
| Vertex figure | |
| Coxeter groups | D6, [33,1,1] |
| Properties | convex |
Alternate names
- Cantellated 6-demicube
- Cantellated demihexeract
- Small rhombated hemihexeract (Acronym: sirhax) (Jonathan Bowers)[1]
Cartesian coordinates
The Cartesian coordinates for the vertices of a runcic 6-cube centered at the origin are coordinate permutations:
- (±1,±1,±1,±3,±3,±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
Runcicantic 6-cube
| Runcicantic 6-cube | |
|---|---|
| Type | uniform 6-polytope |
| Schläfli symbol | t0,1,2{3,33,1} h2,3{4,34} |
| Coxeter-Dynkin diagram | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 5760 |
| Vertices | 1920 |
| Vertex figure | |
| Coxeter groups | D6, [33,1,1] |
| Properties | convex |
Alternate names
- Cantitruncated 6-demicube
- Cantitruncated demihexeract
- Great rhombated hemihexeract (Acronym: girhax) (Jonathan Bowers)[2]
Cartesian coordinates
The Cartesian coordinates for the vertices of a runcicantic 6-cube centered at the origin are coordinate permutations:
- (±1,±1,±3,±5,±5,±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] |
Related polytopes
This polytope is based on the 6-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.
There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 are unique: