@ceperez I think I get it, just a little. The three sets of three concentric circles each are basically rotations in three axes, but flattened out. Which means for any given set of three concentric circles, that set will surround the dots representing one face completely and the dots representing another face will be completely outside the circle. So rotating one of the three concentric circles corresponds to leaving those two faces unchanged. Clever! Maybe I could actually learn how to solve it (very slowly) with this diagram in hand.