Isotopic polytope

An isotopic polytope or facet-transitive polytope is a polytope whose facets are identical under its 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.

Isotopic polytopes are fair dice, but there are fair dice that are not isotopic.

In 3 dimensions
As stated above, the regular polyhedra (the Platonic solids and Kepler-Poinsot polyhedra) are isotopic. The duals of the uniform polyhedra are also isotopic, since uniform polytopes are defined as being isogonal. The Catalan solids (duals of the Archimedean solids, a subset of uniform polyhedra) are notable examples of isotopic polyhedra. Isotopic polyhedra can be referred to as "isohedral" or "face-transitive."