Colm Mulcahy's Hamilternion Card Games page http://www.mathsireland.ie/hamilternion made me wonder if there are any games that (a) hinge on the fact that 3D rotation is noncommutative and (b) require only ordinary dice. One idea I like is that we can have one die act on another: if the first die has its m-face facing upward (for m between 1 and 6), we rotate the second die ninety degrees clockwise around the face that shows an m. Note that the operations of the form "rotate this die ninety degrees clockwise around the face that shows an m" generate a group. It's not the usual way we think about rotation groups, since the specified axes are carried along by the object. A fun way to see that this is still associative is to imagine that the operation is "hold the object still and rotate the rest of the universe ninety degrees counterclockwise around the face that shows an m". To make a game that's fun to play, we'd probably want to incorporate a random element. But hey, we have dice! To make a game that's fun to play, we'd probably want players to be able to score "points". But hey, we have dice! Anyone want to suggest a game along these lines that's got elegantly simple rules and is fun to play? Maybe I'll try out a few such games at the upcoming Celebration of Mind. Jim Propp