The icosahedron and dodecahedron are duals of one another: each vertex of one corresponds to a face of the other and vice versa. All convex polyhedra satisfy th

The icosahedron and dodecahedron are duals of one another: each vertex of one corresponds to a face of the other and vice versa. All convex polyhedra satisfy the property that V + F = E + 2, and since the dual polyhedron conserves the quantity V + F, consequently, dual polyhedra have the same number of edges.