## Information on Polyominoes

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 A000105(M1425) in Neil J. Sloane's database of integer sequences.

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 A000104(M1424) in Neil J. Sloane's database of integer sequences.

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:

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It was last updated Wednesday, 10-May-2006 10:32:13 PDT.