Truncated 5-orthoplexes

In five-dimensional geometry, a truncated 5-orthoplex is a convex uniform 5-polytope, being a truncation of the regular 5-orthoplex. There are 4 unique truncations of the 5-orthoplex. Vertices of the truncation 5-orthoplex are located as pairs on the edge of the 5-orthoplex. Vertices of the bitruncated 5-orthoplex are located on the triangular faces of the 5-orthoplex. The third and fourth truncations are more easily constructed as second and first truncations of the 5-cube. Truncated pentacross Truncated triacontaditeron (Acronym: tot) (Jonathan Bowers) Cartesian coordinates for the vertices of a truncated 5-orthoplex, centered at the origin, are all 80 vertices are sign (4) and coordinate (20) permutations of (±2,±1,0,0,0) The truncated 5-orthoplex is constructed by a truncation operation applied to the 5-orthoplex. All edges are shortened, and two new vertices are added on each original edge. The bitruncated 5-orthoplex can tessellate space in the tritruncated 5-cubic honeycomb. Bitruncated pentacross Bitruncated triacontiditeron (acronym: bittit) (Jonathan Bowers) Cartesian coordinates for the vertices of a truncated 5-orthoplex, centered at the origin, are all 80 vertices are sign and coordinate permutations of (±2,±2,±1,0,0) The bitrunacted 5-orthoplex is constructed by a bitruncation operation applied to the 5-orthoplex. This polytope is one of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex.