isohedron
polyhedron with symmetries acting transitively on its faces
archimedean solid
one of the 13 solids (semi-regular convex polyhedrons composed of regular polygons meeting in identical vertices, excluding the 5 Platonic solids (which are composed of only one type of polygon) and excluding the prisms and antiprisms)
regular polyhedron
polyhedron with regular congruent polygons as faces
noble polyhedron
isohedral and isogonal polyhedron
Catalan solid
13 polyhedra; duals of the Archimedean solids