Hexicated 7-cubes


In seven-dimensional geometry, a hexicated 7-cube is a convex uniform 7-polytope, including 6th-order truncations from the regular 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.

Hexicated 7-cube

In seven-dimensional geometry, a hexicated 7-cube is a convex uniform 7-polytope, a hexication of the regular 7-cube, or alternately can be seen as an expansion operation.

Alternate names

Hexitruncated 7-cube

Alternate names

Hexicantellated 7-cube

Alternate names

Hexiruncinated 7-cube

Alternate names

Hexicantitruncated 7-cube

Alternate names

Hexiruncitruncated 7-cube

Alternate names

Hexiruncicantellated 7-cube

In seven-dimensional geometry, a hexiruncicantellated 7-cube is a uniform 7-polytope.

Alternate names

Hexisteritruncated 7-cube

Alternate names

Hexistericantellated 7-cube

Alternate names

Hexipentitruncated 7-cube

Alternate names

Hexiruncicantitruncated 7-cube

Alternate names

Hexistericantitruncated 7-cube

Alternate names

Hexisteriruncitruncated 7-cube

Alternate names

Hexisteriruncicantellated 7-cube

Alternate names

Hexipenticantitruncated 7-cube

Alternate names

Hexipentiruncitruncated 7-cube

Alternate names

Hexisteriruncicantitruncated 7-cube

Alternate names

Hexipentiruncicantitruncated 7-cube

Alternate names

Hexipentistericantitruncated 7-cube

Alternate names

Omnitruncated 7-cube

The omnitruncated 7-cube is the largest uniform 7-polytope in the B7 symmetry of the regular 7-cube. It can also be called the hexipentisteriruncicantitruncated 7-cube which is the long name for the omnitruncation for 7 dimensions, with all reflective mirrors active.

Alternate names