User:Tomruen/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

Alternate names

 * Small rhombated penteract (Acronym: sirn) (Jonathan Bowers)

Coordinates
The Cartesian coordinates of the vertices of a cantellated 5-cube having edge length 2 are all permutations of:


 * $$\left(\pm1,\ \pm1,\ \pm(1+\sqrt{2}),\ \pm(1+\sqrt{2}),\ \pm(1+\sqrt{2})\right)$$

Bicantellated 5-cube
In five-dimensional geometry, a bicantellated 5-cube is a uniform 5-polytope.

Alternate names

 * Bicantellated penteract, bicantellated 5-orthoplex, or bicantellated pentacross
 * Small birhombated penteractitriacontiditeron (Acronym: sibrant) (Jonathan Bowers)

Coordinates
The Cartesian coordinates of the vertices of a bicantellated 5-cube having edge length 2 are all permutations of:
 * (0,1,1,2,2)

Alternate names

 * Tricantitruncated 5-orthoplex / tricantitruncated pentacross
 * Great rhombated penteract (girn) (Jonathan Bowers)

Coordinates
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:


 * $$\left(1,\ 1+\sqrt{2},\ 1+2\sqrt{2},\ 1+2\sqrt{2},\ 1+2\sqrt{2}\right)$$

Alternate names

 * Bicantitruncated penteract
 * Bicantitruncated pentacross
 * Great birhombated penteractitriacontiditeron (Acronym: gibrant) (Jonathan Bowers)

Coordinates
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)

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