Tessa is a simple game played in two cubes placed side by side. Each space in one cube is linked to its counterpart in the other. These extra connections can be considered a fourth dimension, making the board a 4D cube, or a tesseract.
 
The players take turns dropping pieces on the board. When all pieces have been dropped (you have from 3 to 8 pieces, depending on the variant), the players take turns moving them one space orthogonally, capturing any enemy piece in the way. Win by reducing your opponent to a single piece.
 
 
For more games played in higher dimensions, check out Hyperspace, Skava, Superstring, and Wormhole.