In six-dimensional geometry, a truncated 6-cube (or truncated hexeract) is a convex uniform 6-polytope, being a truncation of the regular 6-cube.
There are 5 truncations for the 6-cube. Vertices of the truncated 6-cube are located as pairs on the edge of the 6-cube. Vertices of the bitruncated 6-cube are located on the square faces of the 6-cube. Vertices of the tritruncated 6-cube are located inside the cubic cells of the 6-cube.
The truncated 6-cube may be constructed by truncating the vertices of the 6-cube at of the edge length. A regular 5-simplex replaces each original vertex.
The Cartesian coordinates of the vertices of a truncated 6-cube having edge length 2 are the permutations of:
The truncated 6-cube, is fifth in a sequence of truncated hypercubes:
The Cartesian coordinates of the vertices of a bitruncated 6-cube having edge length 2 are the permutations of:
The bitruncated 6-cube is fourth in a sequence of bitruncated hypercubes:
The Cartesian coordinates of the vertices of a tritruncated 6-cube having edge length 2 are the permutations of:
The table below contains a set of 63 uniform 6-polytopes generated from the B<sub>6</sub> Coxeter plane, including the regular 6-cube and 6-orthoplex.