This article is about the mathematical polygon. For the game, see
dominoes.
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]
Dominos can tile the plane in a countably infinite number of ways. The number of tilings of a 2×n rectangle with dominoes is , the nth
Fibonacci number.[5]
Domino tilings figure in several celebrated problems, including the
Aztec diamond problem in which large diamond-shaped regions have a number of tilings equal to a
power of two,[6] with most tilings appearing random within a central circular region and having a more regular structure outside of this "arctic circle", and the
mutilated chessboard problem, in which removing two opposite corners from a
chessboard makes it impossible to tile with dominoes.[7]
^Mendelsohn, N. S. (2004), "Tiling with dominoes", The College Mathematics Journal, 35 (2), Mathematical Association of America: 115–120,
doi:
10.2307/4146865,
JSTOR4146865.