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.

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 (6th order truncation) of the regular 7-cube, or alternately can be seen as an expansion operation.

Alternate names

 * Small petated hepteract (acronym: ) (Jonathan Bowers)

Alternate names

 * Petitruncated hepteract (acronym: ) (Jonathan Bowers)

Alternate names

 * Petirhombated hepteract (acronym: ) (Jonathan Bowers)

Alternate names

 * Petiprismated hepteract (acronym: ) (Jonathan Bowers)

Alternate names

 * Petigreatorhombated hepteract (acronym: ) (Jonathan Bowers)

Alternate names

 * Petiprismatotruncated hepteract (acronym: ) (Jonathan Bowers)

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

Alternate names

 * Petiprismatorhombated hepteract (acronym: ) (Jonathan Bowers)

Alternate names

 * Peticellitruncated hepteract (acronym: ) (Jonathan Bowers)

Alternate names

 * Peticellirhombihepteract (acronym: ) (Jonathan Bowers)

Alternate names

 * Petiteritruncated hepteract (acronym: ) (Jonathan Bowers)

Alternate names

 * Petigreatoprismated hepteract (acronym: ) (Jonathan Bowers)

Alternate names

 * Peticelligreatorhombated hepteract (acronym: ) (Jonathan Bowers)

Alternate names

 * Peticelliprismatotruncated hepteract (acronym: ) (Jonathan Bowers)

Alternate names

 * Peticelliprismatorhombihepteract (acronym: ) (Jonathan Bowers)

Alternate names

 * Petiterigreatorhombated hepteract (acronym: ) (Jonathan Bowers)

Alternate names

 * Great petacellated hepteract (acronym: ) (Jonathan Bowers)

Alternate names

 * Great petacellated hepteract (acronym: ) (Jonathan Bowers)

Alternate names

 * Petiterigreatoprismated hepteract (acronym: ) (Jonathan Bowers)

Alternate names

 * Petitericelligreatorhombihepteract (acronym: putcagroh) (Jonathan Bowers)

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

 * Great petated hepteract (Acronym: ) (Jonathan Bowers)