Pentellated 6-cubes


In six-dimensional geometry, a pentellated 6-cube is a convex uniform 6-polytope with 5th order truncations of the regular 6-cube.
There are unique 16 degrees of pentellations of the 6-cube with permutations of truncations, cantellations, runcinations, and sterications. The simple pentellated 6-cube is also called an expanded 6-cube, constructed by an expansion operation applied to the regular 6-cube. The highest form, the pentisteriruncicantitruncated 6-cube, is called an omnitruncated 6-cube with all of the nodes ringed. Six of them are better constructed from the 6-orthoplex given at pentellated 6-orthoplex.

Pentellated 6-cube

Alternate names

Pentitruncated 6-cube

Alternate names

Penticantellated 6-cube

Alternate names

Penticantitruncated 6-cube

Alternate names

Pentiruncitruncated 6-cube

Alternate names

Pentiruncicantellated 6-cube

Alternate names

Pentiruncicantitruncated 6-cube

Alternate names

Pentisteritruncated 6-cube

Alternate names

Pentistericantitruncated 6-cube

Alternate names

Omnitruncated 6-cube

The omnitruncated 6-cube has 5040 vertices, 15120 edges, 16800 faces, 8400 cells, 1806 4-faces, and 126 5-faces. With 5040 vertices, it is the largest of 35 uniform 6-polytopes generated from the regular 6-cube.

Alternate names

Full snub 6-cube

The full snub 6-cube or omnisnub 6-cube, defined as an alternation of the omnitruncated 6-cube is not uniform, but it can be given Coxeter diagram and symmetry +, and constructed from 12 snub 5-cubes, 64 snub 5-simplexes, 60 snub tesseract antiprisms, 192 snub 5-cell antiprisms, 160 3-sr duoantiprisms, 240 4-s duoantiprisms, and 23040 irregular 5-simplexes filling the gaps at the deleted vertices.

Related polytopes

These polytopes are from a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.