Vertices of the truncation 7-orthoplex are located as pairs on the edge of the 7-orthoplex.
Vertices of the bitruncated 7-orthoplex are located on the triangular faces of the 7-orthoplex.
Vertices of the tritruncated 7-orthoplex are located inside the tetrahedral cells of the 7-orthoplex.
Cartesian coordinates for the vertices of a truncated 7-orthoplex, centered at the origin, are all 168 vertices are sign (4) and coordinate (42) permutations of There are two Coxeter groups associated with the truncated 7-orthoplex, one with the C7 or [4,35] Coxeter group, and a lower symmetry with the D7 or [34,1,1] Coxeter group.
Cartesian coordinates for the vertices of a bitruncated 7-orthoplex, centered at the origin, are all sign and coordinate permutations of The tritruncated 7-orthoplex can tessellation space in the quadritruncated 7-cubic honeycomb.