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 5-cube

Alternate names

The rectified 5-cube may be constructed from the 5-cube by truncating its vertices at the midpoints of its edges.

Coordinates

The Cartesian coordinates of the vertices of the rectified 5-cube with edge length is given by all permutations of:

Images

Birectified 5-cube

identified it in 1912 as a semiregular polytope, identifying it as Cr52 as a second rectification of a 5-dimensional cross polytope.

Alternate names

  • Birectified 5-cube/penteract
  • Birectified pentacross/5-orthoplex/triacontiditeron
  • Penteractitriacontiditeron
  • Rectified 5-demicube/demipenteract

    Construction and coordinates

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:

Images

Related polytopes

Related polytopes

These polytopes are a part of 31 uniform polytera generated from the regular 5-cube or 5-orthoplex.