Regatta is a combinatorial game for two players. It's the follow-up to Tixel, which itself is a follow-up to Tix.
On a turn, a player can either place a new piece or move one of her own pieces already on the board. Pieces can be placed either side up, effectively mirroring the shape of the piece. The only way to change which side is facing up is by first picking up a piece in one turn (as a bonus move action, see below), and then placing it anew in another turn with the other side facing up.
A piece can be "active" or "inactive"; only active pieces, which are at a 45º angle, may be moved. Making pieces inactive is done by moving next to or passing an active piece.
Chaining moves is important as this temporarily unlocks three additional move types (aside from placing or moving a piece). If a piece that is moved is made inactive at its end position — i.e., it is self-inactivated — a player can take an extra move if she so chooses; aside from placing or moving a piece, she can now remove a piece from the board, activate an inactive piece, or pivot an active piece to reorient it.
Another difference between Regatta and Tix/Tixel is that in Regatta pieces aren't at any time allowed to protrude outside of the board.
There's also a variant that allows the game to be played by three players.