Domino (mathematics)

This article is about the mathematical polygon. For the game, see dominoes.
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 sometimes understood to mean a tile of any shape.[4]

  1. ^ Golomb, Solomon W. (1994). Polyominoes (2nd ed.). Princeton, New Jersey: Princeton University Press. ISBN 0-691-02444-8.
  2. ^ Weisstein, Eric W. "Domino". From MathWorld – A Wolfram Web Resource. Retrieved 2009-12-05.
  3. ^ Redelmeier, D. Hugh (1981). "Counting polyominoes: yet another attack". Discrete Mathematics. 36 (2): 191–203. doi:10.1016/0012-365X(81)90237-5.
  4. ^ Berger, Robert (1966). "The undecidability of the Domino Problem". Memoirs Am. Math. Soc. 66.