I have a Sakai gyro that looks like this: Now I have to find the three main axes of the moment of inertia by considering symmetries. I put the two axes into the picture which I think I know. The first one would be the upright because it is rotating around that axis. The second one would be the one in the plane of the ring because one half of the ring is symmetrical to other half. But where would the third axis lie? I can't seem to find another symmetry. At first I just thought it's at a 90° angle to my second axis, but one half wouldn't be symmetrical to the other half.