Underlying their simple definition are complex and intricate shapes whose properties are still not fully known. There is no known formula for counting the number of polyominoes of a given size, and the ways that polyominoes tile and fit together are still being explored. Polyominoes have been featured in video games such as Tetris, to board games such as Blokus and Patchwork, to pencil puzzles such as Fillomino. Here is the catalog of polyominoes: https://minos.tessera.li/catalog