The five regular polyhedra: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.

Named for Plato, these shapes are the only convex polyhedra which have identical regular polygons for all their faces, and the same number of faces meeting at each vertex.

Closely related to these are the Archimedean solids which have all regular polygons for faces and the same faces in the same order at each vertex, but the faces are of 2 or more types.

Also related are the Johnson solids, all the other convex polyhedra with regular polygons for all their faces but no particular regularity at their vertices.