A polyomino is a generalization of the shape of a domino. The 5 different shapes in the game of Tetris are the 5 possible tetrominoes. Some polyominos can be replicated and made to fit into a rectangle, and some of them require a surprising and irregular arrangement to do so. David wrote a program to search for and verify several of the known minimal polyomino rectangles.
There are some 15- and 19-ominoes which are believed to form rectangles, but the computing resources to search for them would be astronimical because of combinatorial explosion.
Solomon Golomb coined the term polyomino in the early 1950's.
