Hinged Dissection of Polyominoes and Polyforms
نویسندگان
چکیده
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 dk=2e(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.
منابع مشابه
Hinged dissections of polyominoes and polyforms
This paper shows how to hinge together a collection of polygons at vertices in such a way that a single object can be reshaped into any n-omino, for a given value of n. An n-omino is de ned generally as a connected union of n unit squares on the integer grid. Our best dissection uses 2(n 1) polygons. We generalize this result to the connected unions of nonoverlapping equal-size regular k-gons j...
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