Polyhedral Characterization of Reversible Hinged Dissections

03/03/2018

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by   Jin Akiyama, et al.

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We prove that two polygons A and B have a reversible hinged dissection (a chain hinged dissection that reverses inside and outside boundaries when folding between A and B) if and only if A and B are two non-crossing nets of a common polyhedron. Furthermore, monotone hinged dissections (where all hinges rotate in the same direction when changing from A to B correspond exactly to non-crossing nets of a common convex polyhedron. By envelope/parcel magic, it becomes easy to design many hinged dissections.