Rectified 6-cubes

In six-dimensional geometry, a rectified 6-cube is a convex uniform 6-polytope, being a rectification of the regular 6-cube.

There are unique 6 degrees of rectifications, the zeroth being the 6-cube, and the 6th and last being the 6-orthoplex. Vertices of the rectified 6-cube are located at the edge-centers of the 6-cube. Vertices of the birectified 6-cube are located in the square face centers of the 6-cube.

Alternate names

 * Rectified hexeract (acronym: rax) (Jonathan Bowers)

Construction
The rectified 6-cube may be constructed from the 6-cube by truncating its vertices at the midpoints of its edges.

Coordinates
The Cartesian coordinates of the vertices of the rectified 6-cube with edge length $\sqrt{2}$ are all permutations of:
 * $$(0,\ \pm1,\ \pm1,\ \pm1,\ \pm1,\ \pm1)$$

Alternate names

 * Birectified hexeract (acronym: brox) (Jonathan Bowers)
 * Rectified 6-demicube

Construction
The birectified 6-cube may be constructed from the 6-cube by truncating its vertices at the midpoints of its edges.

Coordinates
The Cartesian coordinates of the vertices of the rectified 6-cube with edge length $\sqrt{2}$ are all permutations of:
 * $$(0,\ 0,\ \pm1,\ \pm1,\ \pm1,\ \pm1)$$

Related polytopes
These polytopes are part of a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.