Runcinated 5-orthoplexes

In five-dimensional geometry, a runcinated 5-orthoplex is a convex uniform 5-polytope with 3rd order truncation 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.

Runcinated 5-orthoplex

Alternate names

Runcinated pentacross
Small prismated triacontiditeron

Coordinates

The vertices of the can be made in 5-space, as permutations and sign combinations of:

Runcitruncated 5-orthoplex

Alternate names

Runcitruncated pentacross
Prismatotruncated triacontiditeron

Coordinates

Cartesian coordinates for the vertices of a runcitruncated 5-orthoplex, centered at the origin, are all 80 vertices are sign and coordinate permutations of

Runcicantellated 5-orthoplex

Alternate names

Runcicantellated pentacross
Prismatorhombated triacontiditeron

Coordinates

The vertices of the runcicantellated 5-orthoplex can be made in 5-space, as permutations and sign combinations of:

Runcicantitruncated 5-orthoplex

Alternate names

Runcicantitruncated pentacross
Great prismated triacontiditeron

Coordinates

The Cartesian coordinates of the vertices of a runcicantitruncated 5-orthoplex having an edge length of are given by all permutations of coordinates and sign of:

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 ⁺ or, and constructed from 10 snub 24-cells, 32 snub 5-cells, 40 snub tetrahedral antiprisms, 80 2-3 duoantiprisms, and 960 irregular 5-cells 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.