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Pentomino


Pentominoes

A pentomino is a 5-polyomino. There are 12 free pentominoes, 18 one-sided pentominoes, and 63 fixed pentominoes. The twelve free pentominoes are known by the letters of the alphabet they most closely resemble: f, I, L, N, P, T, U, V, W, X, y, and Z (Gardner 1960, Golomb 1995). Another common naming convention replaces f, I, L, and N with R, O, Q, and S so that all letters from O to Z are used (Berlekamp et al. 1982). In particular, in the game of life cellular automaton, the f-pentomino is always known as the r-pentomino. The I, L, and T pentominoes can also be called the straight pentomino, L-pentomino, and T-pentomino, respectively.


See also

Domino, Hexomino, Heptomino, Octomino, Polyomino, Tetromino, Triomino

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References

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 110-111, 1987.Berlekamp, E. R.; Conway, J. H; and Guy, R. K. Winning Ways for Your Mathematical Plays, Vol. 1: Adding Games, 2nd ed. Wellesley, MA: A K Peters, 2001.Berlekamp, E. R.; Conway, J. H; and Guy, R. K. Winning Ways for Your Mathematical Plays, Vol. 2: Games in Particular. London: Academic Press, 1982.Dudeney, H. E. "The Broken Chessboard." Problem 74 in The Canterbury Puzzles and Other Curious Problems, 7th ed. London: Thomas Nelson and Sons, pp. 119-120, 1949.Gardner, M. "Mathematical Games: About the Remarkable Similarity between the Icosian Game and the Towers of Hanoi." Sci. Amer. 196, 150-156, May 1957.Gardner, M. "Mathematical Games: More About the Shapes that Can Be Made with Complex Dominoes." Sci. Amer. 203, 186-198, Nov. 1960.Golomb, S. W. Polyominoes: Puzzles, Patterns, Problems, and Packings, 2nd ed. Princeton, NJ: Princeton University Press, 1995.Hunter, J. A. H. and Madachy, J. S. Mathematical Diversions. New York: Dover, pp. 80-86, 1975.Update a linkLei, A. "Pentominoes." http://www.cs.ust.hk/~philipl/omino/pento.htmlMadachy, J. S. "Pentominoes: Some Solved and Unsolved Problems." J. Rec. Math. 2, 181-188, 1969.O'Beirne, T. H. "Pentominoes and Hexiamonds." New Scientist 12, 379-380, 1961.Ruskey, F. "Information on Pentomino Puzzles." http://www.theory.csc.uvic.ca/~cos/inf/misc/PentInfo.html.Smith, A. "Pentomino Relationships." http://www.snaffles.demon.co.uk/pentanomes/.Verbuyst, C. "Pentomino." http://home.planetinternet.be/~odettedm/.

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Pentomino

Cite this as:

Weisstein, Eric W. "Pentomino." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Pentomino.html

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