In eight-dimensional geometry, a rectified 8-simplex is a convex uniform 8-polytope, being a rectification of the regular 8-simplex.
Vertices of the trirectified 8-simplex are located in the tetrahedral cell centers of the 8-simplex.
The Cartesian coordinates of the vertices of the rectified 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,0,0,1,1).
The Cartesian coordinates of the vertices of the birectified 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,0,1,1,1).
The Cartesian coordinates of the vertices of the trirectified 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,1,1,1,1).