Stericated 7-simplexes

In seven-dimensional geometry, a stericated 7-simplex is a convex uniform 7-polytope with 4th order truncations (sterication) of the regular 7-simplex.

There are 14 unique sterication for the 7-simplex with permutations of truncations, cantellations, and runcinations.

Alternate names

 * Small cellated octaexon (acronym: sco) (Jonathan Bowers)

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

Alternate names

 * Small bicellated hexadecaexon (acronym: sabach) (Jonathan Bowers)

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

Alternate names

 * Cellitruncated octaexon (acronym: cato) (Jonathan Bowers)

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

Alternate names

 * Bicellitruncated octaexon (acronym: bacto) (Jonathan Bowers)

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

Alternate names

 * Cellirhombated octaexon (acronym: caro) (Jonathan Bowers)

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

Alternate names

 * Bicellirhombihexadecaexon (acronym: bacroh) (Jonathan Bowers)

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

Alternate names

 * Celligreatorhombated octaexon (acronym: cagro) (Jonathan Bowers)

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

Alternate names

 * Bicelligreatorhombated octaexon (acronym: bacogro) (Jonathan Bowers)

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

Alternate names

 * Celliprismated octaexon (acronym: cepo) (Jonathan Bowers)

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

Alternate names

 * Celliprismatotruncated octaexon (acronym: capto) (Jonathan Bowers)

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

Alternate names

 * Celliprismatorhombated octaexon (acronym: capro) (Jonathan Bowers)

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

Alternate names

 * Bicelliprismatotruncated hexadecaexon (acronym: bicpath) (Jonathan Bowers)

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

Alternate names

 * Great cellated octaexon (acronym: gecco) (Jonathan Bowers)

Coordinates
The vertices of the steriruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,2,3,4,5). This construction is based on facets of the steriruncicantitruncated 8-orthoplex.

Alternate names

 * Great bicellated hexadecaexon (gabach) (Jonathan Bowers)

Coordinates
The vertices of the bisteriruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,2,3,4,5,5). This construction is based on facets of the bisteriruncicantitruncated 8-orthoplex.

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