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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… (More)

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 deened generally as a connected union of n unit squares on the integer grid. Our best dissection uses 2n , 1 polygons. We generalize this result to the connected unions of… (More)

- Erik D Demaine, Timothy Chan, U Waterloo, Robert Connelly, Cornell U, Carmen Cortés +51 others
- 2001

I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Acknowledgments My time as a graduate student has been the best period of my life so far, and for that wonderful… (More)

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