Runcinated 5-simplexes
In six-dimensional geometry, a runcinated 5-simplex is a convex uniform 5-polytope with 3rd order truncations of the regular 5-simplex.
There are 4 unique runcinations of the 5-simplex with permutations of truncations, and cantellations.
Runcinated 5-simplex
Alternate names
Coordinates
The vertices of the runcinated 5-simplex can be most simply constructed on a hyperplane in 6-space as permutations of or of, seen as facets of a runcinated 6-orthoplex, or a biruncinated 6-cube respectively.Runcitruncated 5-simplex
Alternate names
- Runcitruncated hexateron
- Prismatotruncated hexateron
Coordinates
The coordinates can be made in 6-space, as 180 permutations of:This construction exists as one of 64 orthant facets of the runcitruncated 6-orthoplex.
Runcicantellated 5-simplex
Alternate names
- Runcicantellated hexateron
- Biruncitruncated 5-simplex/hexateron
- Prismatorhombated hexateron
Coordinates
The coordinates can be made in 6-space, as 180 permutations of:This construction exists as one of 64 orthant facets of the runcicantellated 6-orthoplex.
Runcicantitruncated 5-simplex
Alternate names
- Runcicantitruncated hexateron
- Great prismated hexateron
Coordinates
The coordinates can be made in 6-space, as 360 permutations of:This construction exists as one of 64 orthant facets of the runcicantitruncated 6-orthoplex.