Truncated 7-cubes

In seven-dimensional geometry, a truncated 7-cube is a convex uniform 7-polytope, being a truncation of the regular 7-cube.

There are 6 truncations for the 7-cube. Vertices of the truncated 7-cube are located as pairs on the edge of the 7-cube. Vertices of the bitruncated 7-cube are located on the square faces of the 7-cube. Vertices of the tritruncated 7-cube are located inside the cubic cells of the 7-cube. The final three truncations are best expressed relative to the 7-orthoplex.