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No symmetry of the binary tiling takes the blue tile (in a middle position relative to the yellow tile two levels above it) to the red tile (in an outer position). In the square tiling of the Euclidean plane, every two tiles are positioned in the same way: there is a symmetry of the whole tiling (a translation) that takes one tile to the other ...
Scoring in Mahjong, a game for four players that originated in China, involves the players obtaining points for their hand of tiles, then paying each other based on the differences in their score and who obtained mahjong (won the hand). The points are given a monetary value agreed by the players.
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 ...
This leaves a second residual rectangle r 1 ×r 0, which we attempt to tile using r 1 ×r 1 square tiles, and so on. The sequence ends when there is no residual rectangle, i.e., when the square tiles cover the previous residual rectangle exactly. The length of the sides of the smallest square tile is the GCD of the dimensions of the original ...
The winning tile is from a replacement tile due to a Kong or a Bonus Tile Win by Double-Kong: 槓上槓 (gong3 soeng5gong3) 9 (8 bonus +1 from self-pick) Similar to 'Win by Kong', except that the tile used to make the Kong was itself an extra tile from declaring a Kong Heavenly Hand: 天糊 (tin1 wu4*2) 13: East wins with initial hand Earthly Hand
Hexagonal tiling is the densest way to arrange circles in two dimensions. The honeycomb conjecture states that hexagonal tiling is the best way to divide a surface into regions of equal area with the least total perimeter.
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