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.
E.D. Demaine and M.L. Demaine—Supported in part by NSF ODISSEI grant EFRI-1240383 and NSF Expedition grant CCF-1138967.
J. Itoh—Supported by Grant-in-Aid for Scientific Research(B)(15KT0020) and Scientific Research(C)(26400072).
C. Nara—Supported by Grant-in-Aid for Scientific Research(C)(16K05258).
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Demaine, E.D., Demaine, M.L., Itoh, Ji., Nara, C. (2016). Continuous Flattening of Orthogonal Polyhedra. In: Akiyama, J., Ito, H., Sakai, T., Uno, Y. (eds) Discrete and Computational Geometry and Graphs. JCDCGG 2015. Lecture Notes in Computer Science(), vol 9943. Springer, Cham. https://doi.org/10.1007/978-3-319-48532-4_8
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DOI: https://doi.org/10.1007/978-3-319-48532-4_8
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