Isogonal polytope

An isogonal polytope or vertex-transitive polytope is a polytope whose vertices are identical under its highest symmetry group. In an isogonal polytope, there is a singular vertex figure, and all of the vertices lie on a hypersphere. The dual of an isogonal polytope is an isotopic polytope, which are made out of one facet type. All regular and uniform polytopes are isogonal.

If an isogonal polytope is also isotopic, it is called a noble polytope. Self-dual isogonal polytopes are also noble.