**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)

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Last updated June 1, 2023 by Erik Demaine.