Paper by Erik D. Demaine

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.

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.

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

The paper is 27 pages.

The paper is available in PostScript (671k), gzipped PostScript (210k), and PDF (238k).
See information on file formats.
[Google Scholar search]

Related papers:
CCCG99a (Hinged Dissection of Polyominoes and Polyiamonds)

See also other papers by Erik Demaine.
These pages are generated automagically from a BibTeX file.
Last updated June 13, 2024 by Erik Demaine.