Given an object with rotational axis of symmetry, is there a way to order them? More specifically, given an axis of rotation and angle, we want to decompose it into rotation around different axis of symmetry in a unique manner. How do we do this for objects having orthogonal axis of symmetry and also for objects having non-orthogonal axis of symmetry?
Order need not be in an absolute sense, it can depend on the axis of rotation too. For example, we can order them in increasing order of angle made with axis of rotation. But, this suffers from non-uniqueness when the axis of rotation makes same angle with multiple axis of symmetry.
Thanks a lot!