# polyomino

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 $n$ squares is called an n-omino. For small $n$, 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.

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.

The topic of how many distinct (free or fixed) n-ominoes exist for a given $n$ has been the subject of much research. It is known that the number of free n-ominoes $A_{n}$ grows exponentially. More precisely, it can be proven that $3.72^{n}.

Polyominoes are special instances of polyforms.

 Title polyomino Canonical name Polyomino Date of creation 2013-03-22 15:20:18 Last modified on 2013-03-22 15:20:18 Owner s0 (9826) Last modified by s0 (9826) Numerical id 10 Author s0 (9826) Entry type Definition Classification msc 05B50 Defines n-omino Defines domino Defines tromino Defines tetromino Defines fixed polyomino Defines lattice animal