As the shape of the board is composed of triangles, rather than squares, the movement patterns for the various pieces have needed to be modified so that they can cope with the new style.
PawnsPawns are naturally the weakest pieces on the board, and the most limited in their options for movement and capturing other pieces. As with standard chess, they may only move forward, and must capture pieces moving diagonally. Also like standard chess, if a pawn reaches the opposite side of the board, it may be queened and gains all the movement and capturing properties of a Queen piece.
KnightKnights have the most interesting movement properties of any piece on the board, as they must move parallel to their edges and in an L pattern. In addition, they are not blocked in their movement by other pieces, as long as their final destination is either free, or occupied by an enemy piece, at which point they capture it.
Similar to their counterparts in standard chess, Rooks are the guardians of the edges of the board, and must move in straight lines parallel to the edges of their triangle. Like standard chess, if the spaces between a Rook and the King are free, and they have not moved, then the King may swap places with the Rook in a move called "Castling".
Bishops are similar to Rooks in the way they move, however, they must instead move in line with the points of whatever triangle they occupy, which is the equivalent of diagonal movement in a triangular chess board. This is somewhat clearer when observed in a diagram.
QueenThe most powerful pieces in both standard and triangular chess. Queen movement styles are a combination of the options available to both Rooks and Bishops. Buried in the back of the board, Queen takes somewhat longer to bring into play in triangular chess though. As mentioned previously, Queen may also be created when a Pawn reaches the opposite edge of the board.
It’s the most vital piece in triangular chess. If your King is captured by another piece, then the game is over for your side. When a player threatens another player's piece with theirs, they must announce that they have put that player into "Check". At which point the player must attempt to find a move which causes their King to become unthreatened. In addition, unlike standard chess, since there is a third party's turn in between "Check" and potential "Checkmate", there are rare occasions where a player's King may be taken out of threatened status before their turn even arrives. As mentioned previously, Kings may "Castle" with Rooks if their paths are unobstructed and neither has moved.