User:Tomruen/Runcinated 5-orthoplexes

In five-dimensional geometry, a runcinated 5-orthoplex is a convex uniform 5-polytope with 3rd order truncation (runcination) of the regular 5-orthoplex.

There are 8 runcinations of the 5-orthoplex with permutations of truncations, and cantellations. Four are more simply constructed relative to the 5-cube.

Alternate names

 * Runcinated pentacross
 * Small prismated triacontiditeron (Acronym: spat) (Jonathan Bowers)

Coordinates
The vertices of the can be made in 5-space, as permutations and sign combinations of:
 * (0,1,1,1,2)

Alternate names

 * Runcitruncated pentacross
 * Prismatotruncated triacontiditeron (Acronym: pattit) (Jonathan Bowers)

Coordinates
Cartesian coordinates for the vertices of a runcitruncated 5-orthoplex, centered at the origin, are all 80 vertices are sign (4) and coordinate (20) permutations of
 * (±3,±2,±1,±1,0)

Alternate names

 * Runcicantellated pentacross
 * Prismatorhombated triacontiditeron (Acronym: pirt) (Jonathan Bowers)

Coordinates
The vertices of the runcicantellated 5-orthoplex can be made in 5-space, as permutations and sign combinations of:
 * (0,1,2,2,3)

Alternate names

 * Runcicantitruncated pentacross
 * Great prismated triacontiditeron (gippit) (Jonathan Bowers)

Coordinates
The Cartesian coordinates of the vertices of a runcicantitruncated tesseract having an edge length of √2 are given by all permutations of coordinates and sign of:


 * $$\left(0, 1, 2, 3, 4\right)$$

Snub 5-demicube
The snub 5-demicube defined as an alternation of the omnitruncated 5-demicube is not uniform, but it can be given Coxeter diagram or  and symmetry [32,1,1]+ or [4,(3,3,3)+], and constructed from 32 snub 5-cells, 80 alternated 6-6 duoprisms, 40 icosahedral prisms, 10 snub 24-cells, and 960 irregular tetrahedrons filling the gaps at the deleted vertices.

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