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Hinged Dissection of Polyominoes and Polyforms

Erik D. Demaine·Martin L. Demaine·David Eppstein·Greg N. Frederickson·Erich Friedman
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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 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.

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Erik D. Demaine, Martin L. Demaine, David Eppstein, Greg N. Frederickson, Erich Friedman. 2003-03-23. Hinged Dissection of Polyominoes and Polyforms. https://arxiv.org/abs/cs/9907018

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