Truncated 5-cubes
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. Truncated 5-cube. Construction and coordinates. The "truncated 5-cube" may be constructed by truncating  the vertices of the 5-cube at formula_1 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: Images. 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. Related polytopes. The "truncated 5-cube", is fourth in a sequence of truncated hypercubes: Bitruncated 5-cube. Construction and coordinates. The "bitruncated 5-cube" may be constructed by bitruncating the  vertices of the 5-cube at formula_3 of the edge length. The Cartesian coordinates of the vertices of a "bitruncated 5-cube" having edge length 2 are all permutations of: Related polytopes. The "bitruncated 5-cube" is third in a sequence of bitruncated hypercubes: Related polytopes. This polytope is one of 31 uniform 5-polytope generated from the regular 5-cube or 5-orthoplex.