The real headscratcher comes when you realise that all reversions are equivalent disregarding rotation. That is, reversing left/right is the same as reversing u

The real headscratcher comes when you realise that all reversions are equivalent disregarding rotation. That is, reversing left/right is the same as reversing up/down and rotating around z. You can actually get a up/down mirroring effect (intuitively speaking) by standing on a mirror and holding a piece of paper perpendicular to it. It will look up/down reversed, not left/right.