**Reference**:- Erik D. Demaine, Martin L. Demaine, David Eppstein, and Erich Friedman, “Hinged Dissection of Polyominoes and Polyiamonds”, in
*Proceedings of the 11th Canadian Conference on Computational Geometry (CCCG'99)*, Vancouver, British Columbia, Canada, August 15–18, 1999. **Abstract**:-
This paper shows how to hinge together a collection of polygons at vertices in
such a way that a single object can be reshaped into any
*n*-omino, for a given value of*n*. Anis defined generally as a connected union of*n*-omino*n*unit squares on the integer grid. Our best dissection uses 2 (*n*− 1) polygons. We generalize this result to the connected unions of nonoverlapping equal-size regular*k*-gons joined edge-to-edge, which includes(*n*-iamonds*k*= 3) and(*n*-hexes*k*= 6). Our best dissection uses ⌈*k*/ 2⌉ (*n*− 1) polygons. We also explore polyabolos, that is, connected unions of nonoverlapping equal-size isosceles right triangles joined edge-to-edge, and give a hinged dissection using 4*n*polygons. Finally, we generalize our result about regular polygons to connected unions of nonoverlapping copies of any polygon*P*, all with the same orientation, that join corresponding edges of*P*. This solution uses*k**n*pieces where*k*is the number of vertices of*P*. **Comments**:- This paper is also available from the electronic proceedings as http://www.cs.ubc.ca/conferences/CCCG/elec_proc/fp37.ps.gz. It is also available as arXiv:cs.CG/9970183v1 of the Computing Research Repository (CoRR).
**Updates**:- There is a revised paper with new results and a new coauthor (Greg Frederickson).
**Length**:- The paper is 15 pages.
**Availability**:- The paper is available in PostScript (709k) and gzipped PostScript (198k).
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**Related papers**:- HingedPolyforms (Hinged Dissection of Polyominoes and Polyforms)

See also other papers by Erik Demaine.

Last updated July 23, 2024 by Erik Demaine.