An interesting connection between two polyhedra construction techniques is presented. The first method replaces edges with squares connected at corners. The second method constructs forms using strips or sticks using a strict over-under-under-over pattern. It is shown how these two techniques can be thought of as two possibilities in a continuum of edge deformations. Example constructions are shown for the five Platonic solids, the cuboctahedron, and the icosidodecahedon. A construction using a serpentine edge is also shown.