Hinged Dissection of Polyominoes and Polyforms
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 edgetoedge 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)*(n1). 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 edgetoedge gluing of n congruent copies of P can be hinged into any edgetoedge gluing of n congruent copies of Q.
 Publication:

arXiv eprints
 Pub Date:
 July 1999
 DOI:
 10.48550/arXiv.cs/9907018
 arXiv:
 arXiv:cs/9907018
 Bibcode:
 1999cs........7018D
 Keywords:

 Computer Science  Computational Geometry;
 Computer Science  Discrete Mathematics;
 G.2.1;
 F.2.2
 EPrint:
 27 pages, 39 figures. Accepted to Computational Geometry: Theory and Applications. v3 incorporates several comments by referees. v2 added many new results and a new coauthor (Frederickson)