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- W2145153585 abstract "A hinged dissection of a set of polygons S is a collection of polygonal pieces hinged together at vertices that can be rotated 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 ⌈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." @default.
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- W2145153585 date "2005-06-01" @default.
- W2145153585 modified "2023-09-27" @default.
- W2145153585 title "Hinged dissection of polyominoes and polyforms" @default.
- W2145153585 cites W1983159462 @default.
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- W2145153585 doi "https://doi.org/10.1016/j.comgeo.2004.12.008" @default.
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