004 Mathart - Platonic Solids - Tetrahedron 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 tetrahedron is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.