In seven-dimensional geometry, a truncated 7-cube is a convex uniform 7-polytope, being a truncation of the regular 7-cube.
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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
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
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
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)