Domino (mathematics)
The single free domino
In mathematics, a domino is a polyomino of order 2, that is, a polygon in the plane made of two equal-sized squares connected edge-to-edge.[1] When rotations and reflections are not considered to be distinct shapes, there is only one free domino.
Since it has reflection symmetry, it is also the only one-sided domino (with reflections considered distinct). When rotations are also considered distinct, there are two fixed dominoes: The second one can be created by rotating the one above by 90°.[2][3]
In a wider sense, the term domino is often understood to simply mean a tile of any shape.[4]
See also
- Domino tiling, a covering of a geometric figure with dominoes; these figure in several celebrated problems:
- Aztec diamond problem
- Mutilated chessboard problem, a domino tiling problem concerning an 8×8 chessboard with two deleted squares
- Dominoes, a set of domino-shaped gaming pieces
References
- ↑ Golomb, Solomon W. (1994). Polyominoes (2nd ed.). Princeton, New Jersey: Princeton University Press. ISBN 0-691-02444-8.
- ↑ Weisstein, Eric W. "Domino". From MathWorld – A Wolfram Web Resource. Retrieved 2009-12-05.
- ↑ Redelmeier, D. Hugh (1981). "Counting polyominoes: yet another attack". Discrete Mathematics 36: 191–203. doi:10.1016/0012-365X(81)90237-5.
- ↑ Berger, Robert (1966). "The undecidability of the Domino Problem". Memoirs Am. Math. Soc. 66.
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