Paper by Erik D. Demaine

Jin Akiyama, Erik D. Demaine, and Stefan Langerman, “Polyhedral Characterization of Reversible Hinged Dissections”, Graphs and Combinatorics, volume 36, number 2, 2020, pages 221–229.

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 noncrossing nets of a common polyhedron. Furthermore, monotone reversible hinged dissections (where all hinges rotate in the same direction when changing from A to B) correspond exactly to noncrossing nets of a common convex polyhedron. By envelope/parcel magic, it becomes easy to design many hinged dissections.

This paper is also available as arXiv:1803.01172 and from SpringerLink.

The paper is 9 pages.

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Related papers:
ReversibleHinged_JCDCGGG2017 (Polyhedral Characterization of Reversible Hinged Dissections)

See also other papers by Erik Demaine.
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Last updated June 8, 2021 by Erik Demaine.