Hippogonal

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A hippogonal (pronounced /hɪˈpɒɡənəl/)^{[citation needed]} chess move is a leap m squares in one of the orthogonal directions, and n squares in the other, for any integer values of m and n.^[1] A specific type of hippogonal move can be written (m,n), usually with the smaller number first. A piece making such moves is referred to as a (m,n) hippogonal mover or (m,n) leaper. For example, the knight moves two squares in one orthogonal direction and one in the other, it is a (1,2) hippogonal mover or (1,2) leaper.

For a (m,n) leaper the occupation of others than the destination square plays no role, thus a (2,2) leaper (Alfil) moves to the second square diagonally and may thereby leap over a piece on the first square of the diagonal. A (m,n) leaper can, by the usual convention, move in all directions symmetric to each other, thus e. g. a (1,1) leaper (Ferz) can move in the four directions (1,1), (1,-1), (-1,1) and (-1,-1).

Other hippogonally moving pieces include the camel,^[2] a fairy chess piece, which moves three squares in one direction and one in the other, and thus is a (1,3) hippogonal mover. The Xiangqi horse is a hippogonal stepper and the nightrider is a hippogonal rider.^[3]

The pieces are colourbound if the sum of m and n is even, and change colour with every move otherwise.

• Piececlopedia: Knight by Fergus Duniho and Hans Bodlaender, The Chess Variant Pages

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