Uniform 6-polytope

Graphs of three regular and related uniform polytopes
6-simplex	Truncated 6-simplex		Rectified 6-simplex
Cantellated 6-simplex		Runcinated 6-simplex
Stericated 6-simplex		Pentellated 6-simplex
6-orthoplex	Truncated 6-orthoplex		Rectified 6-orthoplex
Cantellated 6-orthoplex	Runcinated 6-orthoplex		Stericated 6-orthoplex
Cantellated 6-cube		Runcinated 6-cube
Stericated 6-cube		Pentellated 6-cube
6-cube	Truncated 6-cube		Rectified 6-cube
6-demicube	Truncated 6-demicube		Cantellated 6-demicube
Runcinated 6-demicube		Stericated 6-demicube
2₂₁		1₂₂
Truncated 2₂₁		Truncated 1₂₂

In six-dimensional geometry, a uniform 6-polytope is a six-dimensional uniform polytope. A uniform polypeton is vertex-transitive, and all facets are uniform 5-polytopes.

The complete set of convex uniform 6-polytopes has not been determined, but most 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-Dynkin diagrams. Each combination of at least one ring on every connected group of nodes in the diagram produces a uniform 6-polytope.

The simplest uniform polypeta are regular polytopes: the 6-simplex {3,3,3,3,3}, the 6-cube (hexeract) {4,3,3,3,3}, and the 6-orthoplex (hexacross) {3,3,3,3,4}.