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.
- The paper is available in PDF (829k).
- See information on file formats.
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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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