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.
Cartesian coordinates for the vertices of a rectified 7-cube, centered at the origin, edge length 2 {\displaystyle {\sqrt {2}}\ } are all permutations of:
Cartesian coordinates for the vertices of a birectified 7-cube, centered at the origin, edge length 2 {\displaystyle {\sqrt {2}}\ } are all permutations of:
Cartesian coordinates for the vertices of a trirectified 7-cube, centered at the origin, edge length 2 {\displaystyle {\sqrt {2}}\ } are all permutations of:
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