Cantellated 5-cubes
In six-dimensional geometry, a cantellated 5-cube is a convex uniform 5-polytope, being a cantellation of the regular 5-cube. There are 6 unique cantellation for the 5-cube, including truncations. Half of them are more easily constructed from the dual 5-orthoplex Cantellated 5-cube. Coordinates. The Cartesian coordinates of the vertices of a "cantellated 5-cube" having edge length 2 are all permutations of: Bicantellated 5-cube. In five-dimensional geometry, a bicantellated 5-cube is a uniform 5-polytope. Coordinates. The Cartesian coordinates of the vertices of a "bicantellated 5-cube" having  edge length 2 are all permutations of: Cantitruncated 5-cube. Coordinates. The Cartesian coordinates of the vertices of an cantitruncated 5-cube having an edge length of 2 are given by all permutations of coordinates and sign of: Bicantitruncated 5-cube. Coordinates. Cartesian coordinates for the vertices of a bicantitruncated 5-cube, centered at the origin, are all sign and coordinate permutations of Related polytopes. These polytopes are from a set of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex. It is third in a series of cantitruncated hypercubes: