Rectified 5-cubes

In five-dimensional geometry, a rectified 5-cube is a convex uniform 5-polytope, being a rectification of the regular 5-cube. There are 5 degrees of rectifications of a 5-polytope, the zeroth here being the 5-cube, and the 4th and last being the 5-orthoplex. Vertices of the rectified 5-cube are located at the edge-centers of the 5-cube. Vertices of the birectified 5-cube are located in the square face centers of the 5-cube. Rectified penteract (acronym: rin) (Jonathan Bowers) The rectified 5-cube may be constructed from the 5-cube by truncating its vertices at the midpoints of its edges. The Cartesian coordinates of the vertices of the rectified 5-cube with edge length is given by all permutations of: E. L. Elte identified it in 1912 as a semiregular polytope, identifying it as Cr52 as a second rectification of a 5-dimensional cross polytope. Birectified 5-cube/penteract Birectified pentacross/5-orthoplex/triacontiditeron Penteractitriacontiditeron (acronym: nit) (Jonathan Bowers) Rectified 5-demicube/demipenteract The birectified 5-cube may be constructed by birectifying the vertices of the 5-cube at of the edge length. The Cartesian coordinates of the vertices of a birectified 5-cube having edge length 2 are all permutations of: These polytopes are a part of 31 uniform polytera generated from the regular 5-cube or 5-orthoplex.