I may be posting to the wrong forum, if so, please advise. I'm reading a book on rotational symmetry and its relationship to quantum mechanics. The author is talking about rotations of a unit sphere, in particular binary rotations, i.e. rotations of 180 degrees. He says "If a rotation [he then uses notation to specify it need not be binary] has a binary axis perpendicular to it, then the two semiaxes are interchanged by the binary rotation." I don't understand this. Okay, we have a non-binary rotation, say a rotation in the x-y plane. The z-axis is then an axis perpendicular to this rotation. We can make a binary (= 180 deg) rotation around z. What does it mean to say the "semiaxes are interchanged?" I've googled "semiaxes" and it refers usuall to the axes of an ellipse. What does it mean here? He then says that if the first rotation is itself binary, then the rotation is called a "bilateral binary rotation." Any help appreciated.