Runcinated 5-cubes

In five-dimensional geometry, a runcinated 5-cube is a convex uniform 5-polytope that is a runcination (a 3rd order truncation) of the regular 5-cube. There are 8 unique degrees of runcinations of the 5-cube, along with permutations of truncations and cantellations. Four are more simply constructed relative to the 5-orthoplex. Small prismated penteract (Acronym: span) (Jonathan Bowers) The Cartesian coordinates of the vertices of a runcinated 5-cube having edge length 2 are all permutations of: Runcitruncated penteract Prismatotruncated penteract (Acronym: pattin) (Jonathan Bowers) The Cartesian coordinates of the vertices of a runcitruncated 5-cube having edge length 2 are all permutations of: Runcicantellated penteract Prismatorhombated penteract (Acronym: prin) (Jonathan Bowers) The Cartesian coordinates of the vertices of a runcicantellated 5-cube having edge length 2 are all permutations of: Runcicantitruncated penteract Biruncicantitruncated pentacross great prismated penteract () (Jonathan Bowers) The Cartesian coordinates of the vertices of a runcicantitruncated 5-cube having an edge length of 2 are given by all permutations of coordinates and sign of: These polytopes are a part of a set of 31 uniform polytera generated from the regular 5-cube or 5-orthoplex.