Rules: Both kings must be in check simultaneously. Pawns are promoted when they reach one of the opponent's home rows.
Movement: Basically the same but you can do it in 3d. Pawns are a bit tricky. See http://en.wikipedia.org/wiki/Cubic_chess#Piece_movement.
Because the forum's font screws up the game board so much, we shall be using pictures! (Be sure to only show thumbnails, the picture is quite large.)
EDIT: It is a cube. 8x8x8. The light grey board is the "bottom", and the dark grey board is the "top".





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