Polyhedral Characterization of Reversible Hinged Dissections

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 (w...

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Bibliographic Details
Published in:Graphs and combinatorics 2020-03, Vol.36 (2), p.221-229
Main Authors: Akiyama, Jin, Demaine, Erik D., Langerman, Stefan
Format: Article
Language:English
Subjects:
Combinatorics
Dissection
Engineering Design
Mathematics
Mathematics and Statistics
Original Paper
Polyhedra
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Summary: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.
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-019-02041-2