Hexicated 7-cubes
In seven-dimensional geometry, a hexicated 7-cube is a convex uniform 7-polytope, including 6th-order truncations (hexication) from the regular 7-cube.
| Orthogonal projections in B4 Coxeter plane | |||
|---|---|---|---|
7-cube |
Hexicated 7-cube |
Hexitruncated 7-cube |
Hexicantellated 7-cube |
Hexiruncinated 7-cube |
Hexicantitruncated 7-cube |
Hexiruncitruncated 7-cube |
Hexiruncicantellated 7-cube |
Hexisteritruncated 7-cube |
Hexistericantellated 7-cube |
Hexipentitruncated 7-cube |
Hexiruncicantitruncated 7-cube |
Hexistericantitruncated 7-cube |
Hexisteriruncitruncated 7-cube |
Hexisteriruncicantellated 7-cube |
Hexipenticantitruncated 7-cube |
Hexipentiruncitruncated 7-cube |
Hexisteriruncicantitruncated 7-cube |
Hexipentiruncicantitruncated 7-cube |
Hexipentistericantitruncated 7-cube |
Hexipentisteriruncicantitruncated 7-cube (Omnitruncated 7-cube) | |||
There are 32 hexications for the 7-cube, including all permutations of truncations, cantellations, runcinations, sterications, and pentellations. 20 are represented here, while 12 are more easily constructed from the 7-orthoplex.
The simple hexicated 7-cube is also called an expanded 7-cube, with only the first and last nodes ringed, is constructed by an expansion operation applied to the regular 7-cube. The highest form, the hexipentisteriruncicantitruncated 7-cube is more simply called a omnitruncated 7-cube with all of the nodes ringed.
These polytope are among a family of 127 uniform 7-polytopes with B7 symmetry.