Truncated 6-orthoplexes

In six-dimensional geometry, a truncated 6-orthoplex is a convex uniform 6-polytope, being a truncation of the regular 6-orthoplex.

There are 5 degrees of truncation for the 6-orthoplex. Vertices of the truncated 6-orthoplex are located as pairs on the edge of the 6-orthoplex. Vertices of the bitruncated 6-orthoplex are located on the triangular faces of the 6-orthoplex. Vertices of the tritruncated 6-orthoplex are located inside the tetrahedral cells of the 6-orthoplex.

Alternate names

 * Truncated hexacross
 * Truncated hexacontatetrapeton (Acronym: tag) (Jonathan Bowers)

Construction
There are two Coxeter groups associated with the truncated hexacross, one with the C6 or [4,3,3,3,3] Coxeter group, and a lower symmetry with the D6 or [33,1,1] Coxeter group.

Coordinates
Cartesian coordinates for the vertices of a truncated 6-orthoplex, centered at the origin, are all 120 vertices are sign (4) and coordinate (30) permutations of
 * (±2,±1,0,0,0,0)

Alternate names

 * Bitruncated hexacross
 * Bitruncated hexacontatetrapeton (Acronym: botag) (Jonathan Bowers)

Related polytopes
These polytopes are a part of a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.