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In geometry, a domino tiling of a region in the Euclidean plane is a tessellation of the region by dominoes, shapes formed by the union of two unit squares meeting edge-to-edge. Equivalently, it is a perfect matching in the grid graph formed by placing a vertex at the center of each square of the region and connecting two vertices when they ...
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 ...
There are two uncompleted hexagons of five tiles, also with corner values of 1 at the center. One could be completed with the 1-1-3 tile, and the other cannot be completed, as the required tile would be 0-2-1, which does not exist. Triominoes is a variant of dominoes using triangular tiles published in 1965.
A tiling with rectangles is a tiling which uses rectangles as its parts. The domino tilings are tilings with rectangles of 1 × 2 side ratio. The tilings with straight polyominoes of shapes such as 1 × 3, 1 × 4 and tilings with polyominoes of shapes such as 2 × 3 fall also into this category.
Triangular Dominoes is a variant of dominoes using equilateral triangle tiles, patented by Franklin H. Richards in 1885. Two versions were made: a starter set of 35 unique tiles, with each side numbered from zero to four pips, and an advanced set of 56 unique tiles, with each side numbered from zero to five pips.
Following Grünbaum and Shephard (section 1.3), a tiling is said to be regular if the symmetry group of the tiling acts transitively on the flags of the tiling, where a flag is a triple consisting of a mutually incident vertex, edge and tile of the tiling. This means that, for every pair of flags, there is a symmetry operation mapping the first ...
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A tile-based game is a game that uses tiles as one of the fundamental elements of play. Traditional tile-based games use small tiles as playing pieces for gambling or entertainment games. Some board games use tiles to create their board, giving multiple possibilities for board layout, or allowing changes in the board geometry during play.