Paper by Erik D. Demaine

Reference:
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.

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.

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

Length:
The paper is 9 pages.

Availability:
The paper is available in PDF (829k).
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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.