In geometry, a quasiregular polyhedron is a uniform polyhedron that has exactly two kinds of regular faces, which alternate around each vertex. They are vertex-transitive and edge-transitive, hence a step closer to regular polyhedra than the semiregular, which are merely vertex-transitive.
Image: Rhombicdodecahedron
In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive. It follows that all vertices are congruent.
Platonic solid: Tetrahedron
Image: Tetrakishexahedron
Image: Disdyakisdodecahedron
Image: Disdyakistriacontahedron