Volume 9, Issue 3
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Polyominoes and Related Families
In 1953, when delivering a talk at the Harvard Mathematics Club, mathematician Solomon Golomb  defined a new class of geometric figures he named polyominoes. Polyominoes are generalizations of dominoes  and have been extremely popular since their use in the game of Tetris . They have also enjoyed a prominent place in the recreational mathematics literature since Martin Gardner further popularized them in 1957.
A polyomino is any connected figure that can be constructed by joining congruent squares side by side. A polyomino formed by n squares is referred to as an n-omino. In the first part of this work, we generate all n-ominoes and extend our method to the corresponding generation of polyiamonds, polyhexes, and polykites . In the second part, we will tessellate rectangles using polyominoes and introduce the family of rep-tiles.
Some sections of this work are ordered so that we can compare performance issues among different computer configurations and also calculate timings for a 2003-vintage model 2.4 GHz personal computer using Mathematica 5.
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