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. Runcinated pentacross Small prismated triacontiditeron (Acronym: spat) (Jonathan Bowers) The vertices of the can be made in 5-space, as permutations and sign combinations of: (0,1,1,1,2) Runcitruncated pentacross Prismatotruncated triacontiditeron (Acronym: pattit) (Jonathan Bowers) 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) Runcicantellated pentacross Prismatorhombated triacontiditeron (Acronym: pirt) (Jonathan Bowers) The vertices of the runcicantellated 5-orthoplex can be made in 5-space, as permutations and sign combinations of: (0,1,2,2,3) Runcicantitruncated pentacross Great prismated triacontiditeron (gippit) (Jonathan Bowers) 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: 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 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. This polytope is one of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex.