Runcinated 6-simplexes

In six-dimensional geometry, a runcinated 6-simplex is a convex uniform 6-polytope constructed as a runcination (3rd order truncations) of the regular 6-simplex.

There are 8 unique runcinations of the 6-simplex with permutations of truncations, and cantellations.

Alternate names

 * Small prismated heptapeton (Acronym: spil) (Jonathan Bowers)

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

Alternate names

 * Small biprismated tetradecapeton (Acronym: sibpof) (Jonathan Bowers)

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

Alternate names

 * Prismatotruncated heptapeton (Acronym: patal) (Jonathan Bowers)

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

Alternate names

 * Biprismatorhombated heptapeton (Acronym: bapril) (Jonathan Bowers)

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

Alternate names

 * Prismatorhombated heptapeton (Acronym: pril) (Jonathan Bowers)

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

Alternate names

 * Runcicantitruncated heptapeton
 * Great prismated heptapeton (Acronym: gapil) (Jonathan Bowers)

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

Alternate names

 * Biruncicantitruncated heptapeton
 * Great biprismated tetradecapeton (Acronym: gibpof) (Jonathan Bowers)

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

Related uniform 6-polytopes
The truncated 6-simplex is one of 35 uniform 6-polytopes based on the [3,3,3,3,3] Coxeter group, all shown here in A6 Coxeter plane orthographic projections.