Polyhedral Characterization of Reversible Hinged Dissections
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373_2019_2041_ReferencePDF.pdf
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Author(s)
Akiyama, Jin
Demaine, Erik D
Langerman, Stefan
Date Issued
May 2019
Publisher
Springer Japan
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00373-019-02041-2
