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

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.

Images

Runcitruncated 5-simplex

Alternate names

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.

Images

Runcicantellated 5-simplex

Alternate names

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.

Images

Runcicantitruncated 5-simplex

Alternate names

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.

Images

Related uniform 5-polytopes

These polytopes are in a set of 19 uniform 5-polytopes based on the Coxeter group, all shown here in A5 Coxeter plane orthographic projections.