Domino (mathematics)

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.

[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.

[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.