Vertices of the truncation 7-simplex are located as pairs on the edge of the 7-simplex.
Vertices of the bitruncated 7-simplex are located on the triangular faces of the 7-simplex.
Vertices of the tritruncated 7-simplex are located inside the tetrahedral cells of the 7-simplex.
The vertices of the truncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,0,1,2).
The vertices of the bitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,1,2,2).