Isotopic polytope

An isotopic polytope or facet-transitive polytope is a polytope whose facets are identical under its highest symmetry group. In an isotopic polytope, all of its facets are tangent to a hypersphere. The dual of an isotopic polytope is an isogonal polytope, which are made out of one vertex type. All regular polytopes are isotopic.

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