Paper by Erik D. Demaine

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.

BibTeX

@Article{ReversibleHinged_GC,
  AUTHOR        = {Jin Akiyama and Erik D. Demaine and Stefan Langerman},
  TITLE         = {Polyhedral Characterization of Reversible Hinged Dissections},
  JOURNAL       = {Graphs and Combinatorics},
  journalurl    = {http://www.springer.com/mathematics/numbers/journal/373},
  VOLUME        = 36,
  NUMBER        = 2,
  YEAR          = 2020,
  PAGES         = {221--229},

  length        = {9 pages},
  replaces      = {ReversibleHinged_JCDCGGG2017},
  papers        = {ReversibleHinged_JCDCGGG2017},
  doi           = {https://dx.doi.org/10.1007/s00373-019-02041-2},
  dblp          = {https://dblp.org/rec/journals/gc/AkiyamaDL20},
  comments      = {This paper is also available as <A HREF="https://arXiv.org/abs/1803.01172">arXiv:1803.01172</A> and from <A HREF="https://doi.org/10.1007/s00373-019-02041-2">SpringerLink</A>.},
}

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)