The board can be imagined as a cylinder with no horizontal edges on either side.
The board can be imagined as being wrapped around a cylinder resulting in a board with no horizontal edges. Therefore, the H file sits next to the A file, and pieces can move freely (and give check) from side of the board to he other.
This variant is played from the standard starting position of Standard Chess.
All pieces move just as in Standard Chess but with the added ability to traverse around the cylinder. As we play Cylinder Chess on a traditional flat board, not an actual cylinder, we must move the pieces from the A File to the H File as if they were joined.
Pieces can even capture and mate around the cylinder too. Note the pawn capture from H to A. Also that the Rook at C2 can capture both black Pawns at E2 and F2 - one from each direction!
Pieces can not return to their starting position, which would effectively be not moving at all!
Pawn promotion rules remains the same as Standard Chess.
Normal Standard Chess castling rules apply, even though it is of questionable value in Cylinder Chess
En passant rules remains the same as Standard Chess.
Check and Checkmate rules remain the same as Standard Chess.
Stalemate conditions remain the same as Standard Chess.
Draw conditions remain the same as Standard Chess.
Winning conditions remain the same as Standard Chess.