Truncated 8-cubes

In eight-dimensional geometry, a truncated 8-cube is a convex uniform 8-polytope, being a truncation of the regular 8-cube.

There are unique 7 degrees of truncation for the 8-cube. Vertices of the truncation 8-cube are located as pairs on the edge of the 8-cube. Vertices of the bitruncated 8-cube are located on the square faces of the 8-cube. Vertices of the tritruncated 7-cube are located inside the cubic cells of the 8-cube. The final truncations are best expressed relative to the 8-orthoplex.

Alternate names

 * Truncated octeract (acronym tocto) (Jonathan Bowers)

Coordinates
Cartesian coordinates for the vertices of a truncated 8-cube, centered at the origin, are all 224 vertices are sign (4) and coordinate (56) permutations of
 * (±2,±2,±2,±2,±2,±2,±1,0)

Related polytopes
The truncated 8-cube, is seventh in a sequence of truncated hypercubes:

Alternate names

 * Bitruncated octeract (acronym bato) (Jonathan Bowers)

Coordinates
Cartesian coordinates for the vertices of a truncated 8-cube, centered at the origin, are all the sign coordinate permutations of
 * (±2,±2,±2,±2,±2,±1,0,0)

Related polytopes
The bitruncated 8-cube is sixth in a sequence of bitruncated hypercubes:

Alternate names

 * Tritruncated octeract (acronym tato) (Jonathan Bowers)

Coordinates
Cartesian coordinates for the vertices of a truncated 8-cube, centered at the origin, are all the sign coordinate permutations of
 * (±2,±2,±2,±2,±1,0,0,0)

Alternate names

 * Quadritruncated octeract (acronym oke) (Jonathan Bowers)

Coordinates
Cartesian coordinates for the vertices of a bitruncated 8-orthoplex, centered at the origin, are all sign and coordinate permutations of
 * (±2,±2,±2,±2,±1,0,0,0)