In five-dimensional geometry, a truncated 5-cube is a convex uniform 5-polytope, being a truncation of the regular 5-cube.
There are four unique truncations of the 5-cube. Vertices of the truncated 5-cube are located as pairs on the edge of the 5-cube. Vertices of the bitruncated 5-cube are located on the square faces of the 5-cube. The third and fourth truncations are more easily constructed as second and first truncations of the 5-orthoplex.
The truncated 5-cube may be constructed by truncating the vertices of the 5-cube at of the edge length. A regular 5-cell is formed at each truncated vertex.
The Cartesian coordinates of the vertices of a truncated 5-cube having edge length 2 are all permutations of:
The truncated 5-cube is constructed by a truncation applied to the 5-cube. All edges are shortened, and two new vertices are added on each original edge.
The truncated 5-cube, is fourth in a sequence of truncated hypercubes:
The bitruncated 5-cube may be constructed by bitruncating the vertices of the 5-cube at of the edge length.
The Cartesian coordinates of the vertices of a bitruncated 5-cube having edge length 2 are all permutations of:
The bitruncated 5-cube is third in a sequence of bitruncated hypercubes:
The truncated 5-cube and bitruncated 5-cube are from the family of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex.