A card game based on the Hoffman-Singleton graph, one of the most symmetrical objects in mathematics. Each card is connected to exactly 7 other cards by simple rules. Any two non-joined cards are connected by a unique card. The smallest cycles of connections are pentagons. With these connections, people must find sets of connected cards, much like Set. Whoever collects the most cards wins.
Picture of cards at
http://mathpuzzle.com/facecards.jpg
Larger description of game at
http://www.maa.org/editorial/mathgames/mathgames_11_01_04.html