Pentellated 7-simplexes

In seven-dimensional geometry, a pentellated 7-simplex is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-simplex.

There are 16 unique pentellations of the 7-simplex with permutations of truncations, cantellations, runcinations, and sterications.

Alternate names

 * Small terated octaexon (acronym: seto) (Jonathan Bowers)

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

Alternate names

 * Teritruncated octaexon (acronym: teto) (Jonathan Bowers)

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

Alternate names

 * Terirhombated octaexon (acronym: tero) (Jonathan Bowers)

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

Alternate names

 * Terigreatorhombated octaexon (acronym: tegro) (Jonathan Bowers)

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

Alternate names

 * Teriprismated octaexon (acronym: tepo) (Jonathan Bowers)

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

Alternate names

 * Teriprismatotruncated octaexon (acronym: tapto) (Jonathan Bowers)

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

Alternate names

 * Teriprismatorhombated octaexon (acronym: tapro) (Jonathan Bowers)

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

Alternate names

 * Terigreatoprismated octaexon (acronym: tegapo) (Jonathan Bowers)

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

Alternate names

 * Tericellated octaexon (acronym: teco) (Jonathan Bowers)

Coordinates
The vertices of the pentistericated 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 pentistericated 8-orthoplex.

Alternate names

 * Tericellitruncated octaexon (acronym: tecto) (Jonathan Bowers)

Coordinates
The vertices of the pentisteritruncated 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 pentisteritruncated 8-orthoplex.

Alternate names

 * Tericellirhombated octaexon (acronym: tecro) (Jonathan Bowers)

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

Alternate names

 * Tericelligreatorhombated octaexon (acronym: tecagro) (Jonathan Bowers)

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

Alternate names

 * Bipenticantitruncated 7-simplex as t1,2,3,6{3,3,3,3,3,3}
 * Tericelliprismated octaexon (acronym: tacpo) (Jonathan Bowers)

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

Alternate names

 * Tericelliprismatotruncated octaexon (acronym: tacpeto) (Jonathan Bowers)

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

Alternate names

 * Bipentiruncicantitruncated 7-simplex as t1,2,3,4,6{3,3,3,3,3,3}
 * Tericelliprismatorhombated octaexon (acronym: tacpro) (Jonathan Bowers)

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

Alternate names

 * Great terated octaexon (acronym: geto) (Jonathan Bowers)

Coordinates
The vertices of the pentisteriruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,2,3,4,5,6). This construction is based on facets of the pentisteriruncicantitruncated 8-orthoplex.

Related polytopes
These polytopes are a part of a set of 71 uniform 7-polytopes with A7 symmetry.