A polyomino consists of a number of identical connected squares placed in distinct locations in the plane so that at least one side of each square is adjacent to (i.e. completely coincides with the side of) another square (if the polyomino consists of at least two squares).

A polyomino with squares is called an n-omino. For small , polyominoes have special names. A 1-omino is called a monomino, a 2-omino a domino, a 3-omino a tromino or triomino, etc. The famous Tetris video game derives its name from the fact that the bricks are tetrominoes or 4-ominoes.

Figure: All distinct 1-, 2-, 3-, 4-, and 5-ominoes. Pentominoes have been scaled in the figure to fit on the page.

Fixed polyominoes (which are also called lattice animals) are considered distinct if they cannot be translated into each other, while free polyominoes must also be distinct under rotation and reflection.

Figure: All distinct, fixed dominoes and trominoes.

The topic of how many distinct (free or fixed) n-ominoes exist for a given has been the subject of much research. It is known that the number of free n-ominoes grows exponentially. More precisely, it can be proven that .

Polyominoes are special instances of polyforms.