014 Mathart - Platonic Solids - Icosahedron 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. An icosahedron is a polyhedron with 20 faces, 30 edges and 12 vertices.