**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. **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 Polyiamonds)

See also other papers by Erik Demaine.

Last updated July 23, 2024 by Erik Demaine.