Paper by Erik D. Demaine

Reference:

Erik D. Demaine, Martin L. Demaine, David Eppstein, Greg N. Frederickson, and Erich Friedman, “Hinged Dissection of Polyominoes and Polyforms”, Computational Geometry: Theory and Applications, volume 31, number 3, June 2005, pages 237–262. Special issue of selected papers from the 11th Canadian Conference on Computational Geometry, 1999.

BibTeX

@Article{HingedPolyforms,
  AUTHOR        = {Erik D. Demaine and Martin L. Demaine and David Eppstein and
                   Greg N. Frederickson and Erich Friedman},
  TITLE         = {Hinged Dissection of Polyominoes and Polyforms},
  JOURNAL       = {Computational Geometry: Theory and Applications},
  journalurl    = {https://www.sciencedirect.com/journal/computational-geometry},
  VOLUME        = 31,
  NUMBER        = 3,
  MONTH         = {June},
  YEAR          = 2005,
  PAGES         = {237--262},
  NOTE          = {Special issue of selected papers from the 11th Canadian
                   Conference on Computational Geometry, 1999.},

  length        = {27 pages},
  doi           = {https://dx.doi.org/10.1016/J.COMGEO.2004.12.008},
  dblp          = {https://dblp.org/rec/journals/comgeo/DemaineDEFF05},
  comments      = {This paper is also available as
                   <A HREF="http://arXiv.org/abs/cs.CG/9907018">
                   arXiv:cs.CG/9907018</A> of the
                   <A HREF="http://arXiv.org/archive/cs/intro.html">
                   Computing Research Repository (CoRR)</A>.
                   The paper is also available from
                   <A HREF="http://dx.doi.org/10.1016/j.comgeo.2004.12.008">ScienceDirect</A>.},
  papers        = {CCCG99a; HingedAlphabet},
  replaces      = {CCCG99a},
}

Abstract:

A hinged dissection of a set of polygons S is a collection of polygonal pieces hinged together at vertices that can be folded into any member of S. We present a hinged dissection of all edge-to-edge gluings of n congruent copies of a polygon P that join corresponding edges of P. This construction uses k n pieces, where k is the number of vertices of P. When P is a regular polygon, we show how to reduce the number of pieces to ⌈k / 2⌉ (n − 1). In particular, we consider polyominoes (made up of unit squares), polyiamonds (made up of equilateral triangles), and polyhexes (made up of regular hexagons). We also give a hinged dissection of all polyabolos (made up of right isosceles triangles), which do not fall under the general result mentioned above. Finally, we show that if P can be hinged into Q, then any edge-to-edge gluing of n congruent copies of P can be hinged into any edge-to-edge gluing of n congruent copies of Q.

Comments:

This paper is also available as arXiv:cs.CG/9907018 of the Computing Research Repository (CoRR). The paper is also available from ScienceDirect.

Length:

The paper is 27 pages.

Availability:

The paper is available in PostScript (671k), gzipped PostScript (210k), and PDF (238k).

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Related papers:

CCCG99a (Hinged Dissection of Polyominoes and Polyforms)

HingedAlphabet (Hinged Dissection of the Alphabet)