A *polyomino* of order *n* is an arrangement of *n*
unit squares joined along their edges.
Popular polyominoes include dominoes (*n*=2), tetrominoes (*n=*4),
and pentominoes (*n*=5).

Here is a graphic display of the 5 tetrominoes (remember Tetris?):

The program used to generate polyominoes allows the polyominoes to contain holes. Here are examples of polyominoes with a hole:

The number of *n* cell polyominoes (that allow holes) for *n* = 1,2,...,15, is
1, 1, 2, 5, 12, 35, 108, 369, 1285, 4655, 17073, 63600, 238951,
901971, 3426576.
This is sequence
Anum=A000105">
**A000105**(M1425) in

The number of *n* cell polyominoes (without holes) for *n* = 1,2,...,15, is
1, 1, 2, 5, 12, 35, 107, 363, 1248, 4460, 16094, 58937, 217117, 805475, 3001211.
This is sequence
Anum=A000104">
**A000104**(M1424) in

The program used is due to John Boyer, and is based on a paper of Redelmeier (Discrete Math. 36 (1981) 191-203).

- David Eppsteins Geometry Junkyard entry on polyominoes and other Animals.
- Jan Kok's Polyomino Problems.
- Rodolfo Kurchan runs a magazine Puzzle Fun that is devoted to puzzles involving polyominoes.
- The company Kadon Enterprises "Gamepuzzles" markets some high quality pentomino ("Quintillions") and related puzzles, including 3-D pieces, hexominoes, heptominoes, and even octominoes!
- Andrew L. Clarke created a site called The Poly Pages that contains a wealth of information about Polyominoes and other "polyforms".

Programs available:

It was last updated .