Truncated 8-simplexes

In eight-dimensional geometry, a truncated 8-simplex is a convex uniform 8-polytope, being a truncation of the regular 8-simplex.

There are four unique degrees of truncation. Vertices of the truncation 8-simplex are located as pairs on the edge of the 8-simplex. Vertices of the bitruncated 8-simplex are located on the triangular faces of the 8-simplex. Vertices of the tritruncated 8-simplex are located inside the tetrahedral cells of the 8-simplex.

Alternate names

 * Truncated enneazetton (Acronym: tene) (Jonathan Bowers)

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

Alternate names

 * Bitruncated enneazetton (Acronym: batene) (Jonathan Bowers)

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

Alternate names

 * Tritruncated enneazetton (Acronym: tatene) (Jonathan Bowers)

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

Quadritruncated 8-simplex
The quadritruncated 8-simplex an isotopic polytope, constructed from 18 tritruncated 7-simplex facets.

Alternate names

 * Octadecazetton (18-facetted 8-polytope) (Acronym: be) (Jonathan Bowers)

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

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