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.

Alternate names

 * Pentellated 6-orthoplex
 * Expanded 6-cube, expanded 6-orthoplex
 * Small teri-hexeractihexacontitetrapeton (Acronym: stoxog) (Jonathan Bowers)

Alternate names

 * Teritruncated hexeract (Acronym: tacog) (Jonathan Bowers)

Alternate names

 * Terirhombated hexeract (Acronym: topag) (Jonathan Bowers)

Alternate names

 * Terigreatorhombated hexeract (Acronym: togrix) (Jonathan Bowers)

Alternate names

 * Tericellirhombated hexacontitetrapeton (Acronym: tocrag) (Jonathan Bowers)

Alternate names

 * Teriprismatorhombi-hexeractihexacontitetrapeton (Acronym: tiprixog) (Jonathan Bowers)

Alternate names

 * Terigreatoprismated hexeract (Acronym: tagpox) (Jonathan Bowers)

Alternate names

 * Tericellitrunki-hexeractihexacontitetrapeton (Acronym: tactaxog) (Jonathan Bowers)

Alternate names

 * Tericelligreatorhombated hexeract (Acronym: tocagrax) (Jonathan Bowers)

Omnitruncated 6-cube
The omnitruncated 6-cube has 5040 vertices, 15120 edges, 16800 faces (4200 hexagons and 1260 squares), 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

 * Pentisteriruncicantitruncated 6-cube or 6-orthoplex (omnitruncation for 6-polytopes)
 * Omnitruncated hexeract
 * Great teri-hexeractihexacontitetrapeton (Acronym: gotaxog) (Jonathan Bowers)

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 [4,3,3,3,3]+, and constructed from 12 snub 5-cubes, 64 snub 5-simplexes, 60 snub tesseract antiprisms, 192 snub 5-cell antiprisms, 160 3-sr{4,3} duoantiprisms, 240 4-s{3,4} 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.