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 Small rhombated penteract (Acronym: sirn) (Jonathan Bowers) The Cartesian coordinates of the vertices of a cantellated 5-cube having edge length 2 are all permutations of: In five-dimensional geometry, a bicantellated 5-cube is a uniform 5-polytope. Bicantellated penteract, bicantellated 5-orthoplex, or bicantellated pentacross Small birhombated penteractitriacontiditeron (Acronym: sibrant) (Jonathan Bowers) The Cartesian coordinates of the vertices of a bicantellated 5-cube having edge length 2 are all permutations of: (0,1,1,2,2) Tricantitruncated 5-orthoplex / tricantitruncated pentacross Great rhombated penteract (girn) (Jonathan Bowers) 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: It is third in a series of cantitruncated hypercubes: Bicantitruncated penteract Bicantitruncated pentacross Great birhombated penteractitriacontiditeron (Acronym: gibrant) (Jonathan Bowers) Cartesian coordinates for the vertices of a bicantitruncated 5-cube, centered at the origin, are all sign and coordinate permutations of (±3,±3,±2,±1,0) These polytopes are from a set of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex.