Hinged Dissection of Polyominoes and Polyforms
<|reference_start|>Hinged Dissection of Polyominoes and Polyforms: 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 kn 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 ceiling(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.<|reference_end|>
@article{demaine1999hinged,
    title={Hinged Dissection of Polyominoes and Polyforms},
    author={Erik D. Demaine, Martin L. Demaine, David Eppstein, Greg N.
  Frederickson, Erich Friedman},
    journal={arXiv preprint arXiv:cs/9907018},
    year={1999},
    archivePrefix={arXiv},
    eprint={cs/9907018},
    primaryClass={cs.CG cs.DM}
}