Uniform 5-polytope

Graphs of regular and uniform 5-polytopes.

5-simplex				Rectified 5-simplex				Truncated 5-simplex
Cantellated 5-simplex				Runcinated 5-simplex				Stericated 5-simplex
5-orthoplex				Truncated 5-orthoplex				Rectified 5-orthoplex
Cantellated 5-orthoplex						Runcinated 5-orthoplex
Cantellated 5-cube				Runcinated 5-cube				Stericated 5-cube
5-cube				Truncated 5-cube				Rectified 5-cube
5-demicube						Truncated 5-demicube
Cantellated 5-demicube						Runcinated 5-demicube

In geometry, a uniform 5-polytope is a five-dimensional uniform polytope. By definition, a uniform 5-polytope is vertex-transitive and constructed from uniform 4-polytope facets.

The complete set of convex uniform 5-polytopes has not been determined, but many can be made as Wythoff constructions from a small set of symmetry groups. These construction operations are represented by the permutations of rings of the Coxeter diagrams.