Continuous Flattening of Orthogonal Polyhedra

Can we flatten the surface of any 3-dimensional polyhedron P without cutting or stretching? Such continuous flat folding motions are known when P is convex, but the question remains open for nonconvex polyhedra. In this paper, we give a continuous flat folding motion when the polyhedron P is an orthogonal polyhedron, i.e., when every face is orthogonal to a coordinate axis (x, y, or z). More generally, we demonstrate a continuous flat folding motion for any polyhedron whose faces are orthogonal to the z axis or the xy plane.