Inspiring popular video games like Tetris while contributing to the study of combinotorial geometry and tiling theory, polyominoes have continued to spark interest ever since their inventor, Solomon Golomb, introduced them to puzzle enthusiasts several decades ago. In this fully revised and expanded edition of his landmark book, the author takes a new generation of readers on a mathematical journey into the world of polyominoes, incorporoting the most important recent developments.

Deceptively simple, polyominoes are a collection of squares joined together along their edges. But how many different polyominoes can you make with 5 squares, 6 squares, n squares? If you have a set of pentominoes (shapes consisting of five squares) could you cover a rectangle with them? What would happen if you had cubes instead of squares? Could you pack a box with them?

Posing problems and giving answers along the way, Golomb invites the reader to play with these mathematical structures and develop on understanding of their extraordinary properties. In this new edition, he addresses, for example, the properties of octominoes and enneominoes and the problem of how to cover a donut with polyominoes. An extensive bibliography has been included to guide the reader to other interesting mathematical conundrums and to more advanced mathematical theories of polyominoes.

For professional mathematicians and amateurs seeking further challenge, the author offers a host of new problems that remain to be solved.