Runcinated 8-simplexes

In eight-dimensional geometry, a runcinated 8-simplex is a convex uniform 8-polytope with 3rd order truncations (runcination) of the regular 8-simplex.

There are eleven unique runcinations of the 8-simplex, including permutations of truncation and cantellation. The triruncinated 8-simplex and triruncicantitruncated 8-simplex have a doubled symmetry, showing [18] order reflectional symmetry in the A8 Coxeter plane.

Alternate names

 * Runcinated enneazetton
 * Small prismated enneazetton (Acronym: spene) (Jonathan Bowers)

Coordinates
The Cartesian coordinates of the vertices of the runcinated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,1,1,1,2). This construction is based on facets of the runcinated 9-orthoplex.

Alternate names

 * Biruncinated enneazetton
 * Small biprismated enneazetton (Acronym: sabpene) (Jonathan Bowers)

Coordinates
The Cartesian coordinates of the vertices of the biruncinated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,1,1,1,2,2). This construction is based on facets of the biruncinated 9-orthoplex.

Alternate names

 * Triruncinated enneazetton
 * Small triprismated enneazetton (Acronym: satpeb) (Jonathan Bowers)

Coordinates
The Cartesian coordinates of the vertices of the triruncinated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,1,1,1,2,2,2). This construction is based on facets of the triruncinated 9-orthoplex.

Related polytopes
This polytope is one of 135 uniform 8-polytopes with A8 symmetry.