Truncated 8-orthoplexes

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

There are 7 truncation for the 8-orthoplex. Vertices of the truncation 8-orthoplex are located as pairs on the edge of the 8-orthoplex. Vertices of the bitruncated 8-orthoplex are located on the triangular faces of the 8-orthoplex. Vertices of the tritruncated 7-orthoplex are located inside the tetrahedral cells of the 8-orthoplex. The final truncations are best expressed relative to the 8-cube.

Alternate names

 * Truncated octacross (acronym tek) (Jonthan Bowers)

Construction
There are two Coxeter groups associated with the truncated 8-orthoplex, one with the C8 or [4,3,3,3,3,3,3] Coxeter group, and a lower symmetry with the D8 or [35,1,1] Coxeter group.

Coordinates
Cartesian coordinates for the vertices of a truncated 8-orthoplex, centered at the origin, are all 224 vertices are sign (4) and coordinate (56) permutations of
 * (±2,±1,0,0,0,0,0,0)

Alternate names

 * Bitruncated octacross (acronym batek) (Jonthan Bowers)

Coordinates
Cartesian coordinates for the vertices of a bitruncated 8-orthoplex, centered at the origin, are all sign and coordinate permutations of
 * (±2,±2,±1,0,0,0,0,0)

Alternate names

 * Tritruncated octacross (acronym tatek) (Jonthan Bowers)

Coordinates
Cartesian coordinates for the vertices of a bitruncated 8-orthoplex, centered at the origin, are all sign and coordinate permutations of
 * (±2,±2,±2,±1,0,0,0,0)