Vertices of the truncation 5-simplex are located as pairs on the edge of the 5-simplex.
The vertices of the truncated 5-simplex can be most simply constructed on a hyperplane in 6-space as permutations of (0,0,0,0,1,2) or of (0,1,2,2,2,2).
The vertices of the bitruncated 5-simplex can be most simply constructed on a hyperplane in 6-space as permutations of (0,0,0,1,2,2) or of (0,0,1,2,2,2).
These represent positive orthant facets of the bitruncated 6-orthoplex, and the tritruncated 6-cube respectively.
(Vertices are colored by projection overlap order, red, orange, yellow, green, cyan, blue, purple having progressively more vertices)