Rectified 7-cubes

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

There are unique 7 degrees of rectifications, the zeroth being the 7-cube, and the 6th and last being the 7-cube. Vertices of the rectified 7-cube are located at the edge-centers of the 7-ocube. Vertices of the birectified 7-cube are located in the square face centers of the 7-cube. Vertices of the trirectified 7-cube are located in the cube cell centers of the 7-cube.

Alternate names

 * rectified hepteract (Acronym rasa) (Jonathan Bowers)

Cartesian coordinates
Cartesian coordinates for the vertices of a rectified 7-cube, centered at the origin, edge length $$ \sqrt{2}\ $$ are all permutations of:
 * (±1,±1,±1,±1,±1,±1,0)

Alternate names

 * Birectified hepteract (Acronym bersa) (Jonathan Bowers)

Cartesian coordinates
Cartesian coordinates for the vertices of a birectified 7-cube, centered at the origin, edge length $$ \sqrt{2}\ $$ are all permutations of:
 * (±1,±1,±1,±1,±1,0,0)

Alternate names

 * Trirectified hepteract
 * Trirectified 7-orthoplex
 * Trirectified heptacross (Acronym sez) (Jonathan Bowers)

Cartesian coordinates
Cartesian coordinates for the vertices of a trirectified 7-cube, centered at the origin, edge length $$ \sqrt{2}\ $$ are all permutations of:
 * (±1,±1,±1,±1,0,0,0)