Definition:Polyomino
Definition
A polyomino is a configuration of $n$ unit squares, for a given (strictly) positive integer $n$, which are placed side by side with vertices touching, to form a plane figure.
A polyomino of $n$ squares can be referred to as an $n$-omino.
Free Polyomino
A free polyomino is a polyomino which is not distinguished from its image under a reflection.
That is, it is considered free of the plane in which it is embedded, and can be "lifted up and turned over".
Fixed Polyomino
A fixed polyomino is a polyomino which is distinguished from its image under a reflection.
That is, it is considered fixed in the plane in which it is embedded, and (while it may be translated and rotated in the plane) cannot be "lifted up and turned over".
Also known as
An $n$-omino can also be referred to by the more unwieldy name $n$-polyomino.
Also see
For small $n$, polyominoes have their own names:
- $n = 1$: Monomino
- $n = 2$: Domino
- $n = 3$: Tromino
- $n = 4$: Tetromino
- $n = 5$: Pentomino
- $n = 6$: Hexomino
- $n = 7$: Heptomino
- $n = 8$: Octomino
- Results about polyominoes can be found here.
Linguistic Note
The word polyomino is derived by back-formation from the word domino, which can be defined as a polyomino formed from $2$ unit squares.
Thus a polyomino is a domino which is generalised for $n$ unit squares.
The plural of polyomino is polyominoes.
Sources
- Weisstein, Eric W. "Polyomino." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Polyomino.html