Cantellated 7-simplexes

In seven-dimensional geometry, a cantellated 7-simplex is a convex uniform 7-polytope, being a cantellation of the regular 7-simplex.

There are unique 6 degrees of cantellation for the 7-simplex, including truncations.

Alternate names

 * Small rhombated octaexon (acronym: saro) (Jonathan Bowers)

Coordinates
The vertices of the cantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,1,1,2). This construction is based on facets of the cantellated 8-orthoplex.

Alternate names

 * Small birhombated octaexon (acronym: sabro) (Jonathan Bowers)

Coordinates
The vertices of the bicantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,1,1,2,2). This construction is based on facets of the bicantellated 8-orthoplex.

Alternate names

 * Small trirhombihexadecaexon (stiroh) (Jonathan Bowers)

Coordinates
The vertices of the tricantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,1,2,2,2). This construction is based on facets of the tricantellated 8-orthoplex.

Alternate names

 * Great rhombated octaexon (acronym: garo) (Jonathan Bowers)

Coordinates
The vertices of the cantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,1,2,3). This construction is based on facets of the cantitruncated 8-orthoplex.

Alternate names

 * Great birhombated octaexon (acronym: gabro) (Jonathan Bowers)

Coordinates
The vertices of the bicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,1,2,3,3). This construction is based on facets of the bicantitruncated 8-orthoplex.

Alternate names

 * Great trirhombihexadecaexon (acronym: gatroh) (Jonathan Bowers)

Coordinates
The vertices of the tricantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,2,3,4,4). This construction is based on facets of the tricantitruncated 8-orthoplex.

Related polytopes
This polytope is one of 71 uniform 7-polytopes with A7 symmetry.