Thirteen Archimedean Polyhedra

Theorem
There exist exactly $13$ distinct Archimedean polyhedra:


 * Truncated tetrahedron
 * Cuboctahedron
 * Truncated Cube
 * Truncated octahedron
 * Rhombicuboctahedron
 * Truncated cuboctahedron
 * Snub cube
 * Icosidodecahedron
 * Truncated dodecahedron
 * Truncated icosahedron
 * Rhombicosidodecahedron
 * Truncated icosidodecahedron
 * Snub dodecahedron