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Three player chess game in 7x7x7 cube.  There is one player aligned parallel to each axis.
Kings and Queens move in each of the 26 linear directions around it.
Bishops move in parity even directions (same color).
Rooks move in parity odd directions (alternating colors).
Knights move in a 0x1x2 pattern.
Winged pieces move or capture like a knight, or move (with no capture) in a 1x2x3 pattern.
Pawns move in the three forward directions in the same file as the pawn and capture in one of the 3 forward diagonal directions on either side.

Rules are a work in progess, much like the interface.

There is a possiblity that a player could move, not be in check, then have the next player expose a check from the third player.  The third player would not be able to capture the first player's king in this instance.  Instead, he can use the opportunity to pick up some material, or add to his attack on the first player's king (allowing for double, or even triple, checks).

Of course, this has not been written into the interface, as there is not checking for checks at this time.

 
Source: README, updated 2017-05-04