001 Mathart - Platonic Solids - Cube 01 - 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. The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.