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 us...

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Bibliographic Details
Published in:arXiv.org 2003-03
Main Authors: Demaine, Erik D, Demaine, Martin L, Eppstein, David, Frederickson, Greg N, Friedman, Erich
Format: Article
Language:English
Subjects:
Apexes
Dissection
Edge joints
Gluing
Hexagons
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Summary: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.
ISSN:2331-8422