Runcinated 5-simplexes

In six-dimensional geometry, a runcinated 5-simplex is a convex uniform 5-polytope with 3rd order truncations (Runcination) of the regular 5-simplex. There are 4 unique runcinations of the 5-simplex with permutations of truncations, and cantellations. Runcinated hexateron Small prismated hexateron (Acronym: spix) (Jonathan Bowers) The vertices of the runcinated 5-simplex can be most simply constructed on a hyperplane in 6-space as permutations of (0,0,1,1,1,2) or of (0,1,1,1,2,2), seen as facets of a runcinated 6-orthoplex, or a biruncinated 6-cube respectively. Runcitruncated hexateron Prismatotruncated hexateron (Acronym: pattix) (Jonathan Bowers) The coordinates can be made in 6-space, as 180 permutations of: (0,0,1,1,2,3) This construction exists as one of 64 orthant facets of the runcitruncated 6-orthoplex. Runcicantellated hexateron Biruncitruncated 5-simplex/hexateron Prismatorhombated hexateron (Acronym: pirx) (Jonathan Bowers) The coordinates can be made in 6-space, as 180 permutations of: (0,0,1,2,2,3) This construction exists as one of 64 orthant facets of the runcicantellated 6-orthoplex. Runcicantitruncated hexateron Great prismated hexateron (Acronym: gippix) (Jonathan Bowers) The coordinates can be made in 6-space, as 360 permutations of: (0,0,1,2,3,4) This construction exists as one of 64 orthant facets of the runcicantitruncated 6-orthoplex. These polytopes are in a set of 19 uniform 5-polytopes based on the [3,3,3,3] Coxeter group, all shown here in A5 Coxeter plane orthographic projections.