Perhaps you enjoy M.C. Escher's art, with its visual illusions. An interesting game is to try to decipher exactly what is going on mathematically/geometrically in his creations.
By luck, I found a related game that involves a different form of exploration of M.C. Escher-type designs. Called Adynatopia, the game was invented by Louis (T) and is available through JayIsGames.com.
Your control keys are the four Arrow-keys to move your pawn plus the Spacebar allows you to make "depth-jumps" between structures. In all fourteen levels, the goal is to navigate the 3-D Escher-like structure until your pawn touches the grey pawn. Beware of odd visual effects (or assumptions) that lead you astray from your goal, but that's the challenge of the game. The idea of "above" or "across" take on new meanings perceptually.
After this experience, you may want to try more Escher-type worlds, such as Alexander Bruce's Antichamber, Jacek Szleszyński's Kveendolnitza, GroZZleR's Shift 2, or even GroZZleR's Fractured.
If you know of other mathematics-based games on-line that are rich experiences, please let me know about them so I can share them with others.