011 Mathart - Platonic Solids - Dodecahedron 02 - 10 cm A Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size) regular (all angles equal and all sides equal) polygonal faces with the same number of faces meeting at each vertex. Five solids meet those criteria: Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron. A dodecahedron is a polyhedron with 12 faces, 20 vertices, 30 edges.