Hexagonal chess

Hexagonal chess is a group of chess variants played on boards composed of hexagon cells. The best known is Gliński's variant, played on a symmetric 91-cell hexagonal board. Since each hexagonal cell not on a board edge has six neighbor cells, there is generally increased mobility for pieces (that cannot move diagonally) compared to a standard orthogonal chessboard. For example, a rook on a hexboard usually has six natural directions for movement instead of four in the standard 8×8 board. Three colours are typically used on a hexboard so that no two neighboring cells are the same colour, and a colour-restricted game piece such as the orthodox chess bishop usually comes in sets of three per player in order to maintain the game's balance. Many different shapes and sizes of hexagon-based boards are used as variants. The nature of the game is also affected by the 30° orientation of the board's cells; the board can be horizontally oriented (Wellisch's, de Vasa's, Brusky's) or vertically oriented (Gliński's, Shafran's, McCooey's). When the sides of hexagonal cells face the players, pawns typically have one straightforward move direction. If a variant's gameboard has cell vertices facing the players, pawns typically have two oblique-forward move directions. The possibility of a hexagon-based board with three-fold rotational symmetry has also resulted in a number of three-player variants. Because the six edges and six vertices of regular hexagons are equally spaced, directions can be referenced analogously to the 12 cardinal directions of a clock face. For example, on a board made of horizontally aligned hexagons, the forward and backward directions can be referred to as the "12 o'clock" and "6 o'clock" directions. The first applications of chess on hexagonal boards probably occurred mid-19th century, but two early examples did not include checkmate as the winning objective. More chess-like...