Paper by Erik D. Demaine

Reference:

Erik D. Demaine, Martin L. Demaine, Jin-Ichi Itoh, and Chie Nara, “Continuous flattening of orthogonal polyhedra”, in Revised Papers from the 18th Japan Conference on Discrete and Computational Geometry and Graphs (JCDCGG 2015), Lecture Notes in Computer Science, volume 9943, Kyoto, Japan, September 14–16, 2015, pages 85–93.

Abstract:

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.

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FlatteningOrthogonal_JCDCGG2015 (Continuous flattening of orthogonal polyhedra)