User:Tomruen/Truncated 5-orthoplexes

In six-dimensional geometry, a truncated 5-orthoplex is a convex uniform 5-polytope, being a truncation of the regular 5-orthoplex.

There are 4 unique truncations of the 5-orthoplex. Vertices of the truncation 5-orthoplex are located as pairs on the edge of the 5-orthoplex. Vertices of the bitruncated 5-orthoplex are located on the triangular faces of the 5-orthoplex. The third and fourth truncations are more easily constructed as second and first truncations of the 5-cube.

Alternate names

 * Truncated pentacross
 * Truncated triacontiditeron (Acronym: tot) (Jonathan Bowers)

Coordinates
Cartesian coordinates for the vertices of a truncated 5-orthoplex, centered at the origin, are all 80 vertices are sign (4) and coordinate (20) permutations of
 * (±2,±1,0,0,0)

Images
The trunacted 5-orthoplex is constructed by a truncation operation applied to the 5-orthoplex. All edges are shortened, and two new vertices are added on each original edge.

Bitruncated 5-orthoplex
The bitruncated 5-orthoplex can tessellate space in the tritruncated 5-cubic honeycomb.

Alternate names

 * Bitruncated pentacross
 * Bitruncated triacontiditeron (acronym: gart) (Jonathan Bowers)

Coordinates
Cartesian coordinates for the vertices of a truncated 5-orthoplex, centered at the origin, are all 80 vertices are sign and coordinate permutations of
 * (±2,±2,±1,0,0)

Images
The bitrunacted 5-orthoplex is constructed by a bitruncation operation applied to the 5-orthoplex. All edges are shortened, and two new vertices are added on each original edge.

Related polytopes
This polytope is one of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex.