Geometrically, how do rotations in a cube look? i.e rotate through 180 degrees about the line joining midpoints of opposite edges, how does it look? Are the rotations the different ways of getting from one vertex to the opposite vertex in the cube (where opposite is defined by the line joining opposite edges)? So there are 6 different rotatations in that example. Each of them equally valid. Whereas in a square there are only two way of a rotation by 180 degrees?