In seven-dimensional geometry, a rectified 7-simplex is a convex uniform 7-polytope, being a rectification of the regular 7-simplex.
Vertices of the birectified 7-simplex are located in the triangular face centers of the 7-simplex.
Vertices of the trirectified 7-simplex are located in the tetrahedral cell centers of the 7-simplex.
The trirectified 7-simplex is the intersection of two regular 7-simplexes in dual configuration.
This characterization yields simple coordinates for the vertices of a trirectified 7-simplex in 8-space: the 70 distinct permutations of (1,1,1,1,−1,−1,−1,-1).