Hinged Dissection of Polyominoes and Polyforms

Simple item page
dc.creatorDemaine, Erik D.
dc.creatorDemaine, Martin L.
dc.creatorEppstein, David
dc.creatorFrederickson, Greg N.
dc.creatorFriedman, Erich
dc.date1999-07-10
dc.date2003-03-23
dc.date.accessioned2026-07-07T03:24:14Z
dc.date.available2026-07-07T03:24:14Z
dc.descriptionA 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.
dc.description27 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)
dc.identifierhttps://arxiv.org/abs/cs/9907018
dc.identifierhttp://arxiv.org/abs/cs/9907018
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/33244
dc.subjectComputational Geometry
dc.subjectDiscrete Mathematics
dc.subjectG.2.1; F.2.2
dc.titleHinged Dissection of Polyominoes and Polyforms
dc.typetext

Files

Collections

arXiv