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arXiv · 1803.01172

Polyhedral Characterization of Reversible Hinged Dissections

Jin Akiyama·Erik D. Demaine·Stefan Langerman
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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.

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Jin Akiyama, Erik D. Demaine, Stefan Langerman. 2018-03-03. Polyhedral Characterization of Reversible Hinged Dissections. https://arxiv.org/abs/1803.01172

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