A regular polyhedron is a three-dimensional geometric shape that has congruent regular polygonal faces and identical vertices. Synonyms for regular polyhedron include platonic solid, platonic body, platonic shape, or simply, regular solid. Platonic solids, named for the ancient Greek philosopher Plato, are the five regular polyhedra: tetrahedron, cube, octahedron, dodecahedron, and icosahedron. Another synonym for regular polyhedron is uniform polyhedron, which refers to a polyhedron with the same symmetry group acting transitively on its vertices, edges, and faces. Regular polyhedra have fascinated mathematicians and scientists for centuries and continue to inspire research and artistic expression today.