Isohedron

In geometry, an isohedron is a polyhedron with symmetries acting transitively on its faces. Their topology can be represented by a face configuration. All 5 Platonic solids and 13 Catalan solids are isohedra, as well as the infinite families of trapezohedra and bipyramids. Some forms allow geometric variations including concave and self-intersecting geometries

Convex isohedra make fair dice. An isohedron has an even number of faces.