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.

Alternate names

 * Truncated hepteract (Jonathan Bowers)

Coordinates
Cartesian coordinates for the vertices of a truncated 7-cube, centered at the origin, are all sign and coordinate permutations of
 * (1,1+√2,1+√2,1+√2,1+√2,1+√2,1+√2)

Related polytopes
The truncated 7-cube, is sixth in a sequence of truncated hypercubes:

Alternate names

 * Bitruncated hepteract (Jonathan Bowers)

Coordinates
Cartesian coordinates for the vertices of a bitruncated 7-cube, centered at the origin, are all sign and coordinate permutations of
 * (±2,±2,±2,±2,±2,±1,0)

Related polytopes
The bitruncated 7-cube is fifth in a sequence of bitruncated hypercubes:

Alternate names

 * Tritruncated hepteract (Jonathan Bowers)

Coordinates
Cartesian coordinates for the vertices of a tritruncated 7-cube, centered at the origin, are all sign and coordinate permutations of
 * (±2,±2,±2,±2,±1,0,0)