"And if you think of it like that, Hitler purposely turned it from a "left-facing" swastika to a right-facing/turning (i'm not sure how to call it) one."
Popular claim, but bollucks. The Swastika as used in many European cultures was the 'wrong way' around long before Hitler aledgedly turned it around, indeed the German Hooked Cross was itself a rip off of the Gammadian cross which has been the 'wrong way' around since just after the Roman Empire became christianised.
Incidently in Hinduism the symbol was use facing both ways before Buddhism adopted it.
I wonder how much it would cost to re-tile the floor of the Amiens cathedral, afterall, we wouldn't want people to get offended now would we. And to think that 700 years ago western cathedral builders were turning the symbol the wrong way round, presumably to bring bad luck on people who prayed there, for shame!