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 (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.

• Publication year

  2018

• Venue

  Graphs and Combinatorics

• Publication date

  2018-03-03

• Fields of study

  Mathematics, Materials Science, Computer Science

• Identifiers
  DOI 10.1007/s00373-019-02041-2arXiv 1803.01172
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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