A rectangular polyhedron is a geometric solid, all of whose lateral faces are identical regular polygons, and in which the same number of polygons meet at each vertex. There are only ve regular polyhedrons, or Platonic solids, named according to the number of faces each has; as shown in the gure.Tetrahedron Hexahedron Octahedron Dodecahedron Icosahedron In 1751, Euler proved a formula relating the faces, edges, and vertices of any convex polyhedron, not just a regular one; the result was already known to Descartes a century earlier. For the solids pictured, con rm Euler's formula F C V D E C 2; where F; E, and V denote the number of faces