Regular Polyhedra Regular Polyhedra A polyhedron is a solid figure bounded by polygons. These polygons are called the faces of the polyhedron. Two faces of a polyhedron meet along an edge of the polyhedron, and several faces meet at a corner, or vertex .
All faces are congruent.
Here is Euclid's proof that there are only five regular polyhedra. For a regular polyhedron we will let A be the interior angle of a face at a vertex. All of these angles are equal since the polyhedron is regular. Let p be the number of edges around each face. This number is the same for each face.