Uniform 5-polytope

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.

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

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.

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