I need an original idea for a geometry game!

I need to do one for my math class. It should be a board, or cards, or something like a physical game (not a computer game.) I am going to try and use art that encorporates geometry, such as Picasso’s works.
What I need from the teemings is a few ideas for game mechanics that involve geometry. I had thought about doing random equations, but that would be algebra. Think proofs. I am not trying to get the SD t do my homework; I have racked my brain for ideas, and have come up empty handed.

Thanks in advance for your help!

How about “Tesseracts”? – you play it like “squares”, only in four dimensions.

I am NOT joking. Imagine a 4D grid of points. Playes take turns drawing lines connecting points (no diagonals, though – only along the x, y, z, and – w? — direction. Every time you complete a tesseract you get to put your initials in it. If you can then complete a whole line of tesseracts by adding only one stroke per, you get those, too.

I suppose you could do it in 3Dc a lot easier (wuss!), and it might take a REALLY long time to play in 4D, but it should be possible. I’ve designed 4D game boards for tic-tac toe and simple blocking games.