Runcinated 6-orthoplexes
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In six-dimensional geometry, a runcinated 6-orthplex is a convex uniform 6-polytope with 3rd order truncations (runcination) of the regular 6-orthoplex.
 6-cube     |
 Runcinated 6-cube |
 Biruncinated 6-cube |
 Runcinated 6-orthoplex |
 6-orthoplex |
 Runcitruncated 6-cube |
 Biruncitruncated 6-cube |
 Runcicantellated 6-orthoplex |
 Runcicantellated 6-cube |
 Biruncitruncated 6-orthoplex |
 Runcitruncated 6-orthoplex |
 Runcicantitruncated 6-cube |
 Biruncicantitruncated 6-cube |
 Runcicantitruncated 6-orthoplex | |
| Orthogonal projections in BC6 Coxeter plane | ||||
|---|---|---|---|---|
There are 12 unique runcinations of the 6-orthoplex with permutations of truncations, and cantellations. 7 are expressed relative to the dual 6-cube.
Runcinated 6-orthoplex
Alternate names
- Small prismatohexacontatetrapeton (spog) (Jonathan Bowers)[1]
Images
| 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] |
Runcicantellated 6-orthoplex
Alternate names
- Prismatorhombated hexacontatetrapeton (prog) (Jonathan Bowers)[2]
Images
| 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] |
Biruncitruncated 6-orthoplex
Alternate names
- Biprismatotruncated hexacontatetrapeton (boprax) (Jonathan Bowers)[3]
Images
| 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] |
Runcitruncated 6-orthoplex
Alternate names
- Prismatotruncated hexacontatetrapeton (potag) (Jonathan Bowers)[4]
Images
| 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] |
Runcicantitruncated 6-orthoplex
Alternate names
- Great prismated hexacontatetrapeton (gopog) (Jonathan Bowers)[5]
Images
| 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] |
Related polytopes
These polytopes are from a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube and 6-orthoplex.
