We introduce a novel method for constructing polyhedra by blending together two or more existing polyhedra, using a dualization method. The method results in a Minkowski sum, analogous to that of overlay tilings , which uses a topological dual operation to create tilings from a network (a graph . embedded in a plane). This paper extends that method to networks on the surface of the unit sphere. We begin with polyhedra in canonical form, dualize them to form networks, overlay the networks, and dualize the result to obtain a new polyhedron that blends together the faces of the original polyhedra.