in the notations describing the movement of fairy pieces, and are usually explained separately. Higher dimensions Some three-dimensional chess variants also exist, such as Raumschach, along with pieces that take advantage of the extra dimension on the board. Notations Parlett's movement notation In his book The Oxford History of Board Games David Parlett used a notation to describe fairy piece movements. The move is specified in the form m={expression}, where m stands for "move", and the expression is composed from the following elements: Distance (numbers, n) 1 – a distance of one (i.e. to adjacent square) 2 – a distance of two n – any distance in the given direction Direction (punctuation, X) * – orthogonally or diagonally (all eight possible directions) + – orthogonally (four possible directions) > – orthogonally forwards < – orthogonally backwards <> – orthogonally forwards and backwards = – orthogonally sideways (used here instead of Parlett's divide symbol.) >= – orthogonally forwards or sideways <= – orthogonally backwards or sideways X – diagonally (four possible directions) X> – diagonally forwards X< – diagonally backwards Grouping / – two orthogonal moves separated by a slash denote a hippogonal move (i.e. jumps like a knight) & – repeated movement in the same direction, such as for hippogonal riders (e.g., the nightrider) . – then, (e.g., an aanca is 1X.n+; one step diagonally and then any distance orthogonally outwards) Additions to Parlett's The following can be added to Parlett's to make it more complete: Conditions under which the move may occur (lowercase alphanumeric, except n) (default) – May occur at any point in the game i – May only be made on the initial move (e.g. pawn's 2 moves forward) c – May only be made on a capture (e.g. pawn's diagonal capture) o – May not be used for a capture (e.g. pawn's forward move) Move type (default) – Captures by landing on the piece; blocked by intermediate pieces ~ – Leaper (leaps) ^ – Locust (captures by hopping; implies hopper) Grouping (punctuation) , (comma) – separates move options; only one of the comma-delimited options may be chosen per move () – grouping operator; see nightrider - – range operator The format (not including grouping) is: <conditions> <move type> <distance> <direction> <other> On this basis, the traditional chess moves (excluding castling and en passant capture) are: King: 1* Queen: n* Bishop: nX Rook: n+ Pawn: o1>, c1X>,