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In five-dimensional geometry, a rectified 5-cube is a convex uniform 5-polytope, being a rectification of the regular 5-cube.
Contents
- Alternate names
- Construction
- Coordinates
- Birectified 5 cube
- Construction and coordinates
- Related polytopes
- References
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-ocube are located in the square face centers of the 5-cube.
Alternate names
Construction
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
Birectified 5-cube
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.
Alternate names
Construction and coordinates
The birectified 5-cube may be constructed by birectifing the vertices of the 5-cube at
The Cartesian coordinates of the vertices of a birectified 5-cube having edge length 2 are all permutations of:
Related polytopes
These polytopes are a part of 31 uniform polytera generated from the regular 5-cube or 5-orthoplex.