Ok but if we're going by dictionary definitions

A movable structure used to close off an entrance

Which basically includes half of the universe as well. So the answer to the question becomes: "there is a near infinite, uncountable, amount of wheels in the world, defined as a circle that can rotate; accompanied by a myriad of doors, defined as something that can open or close." Hooray. The question isn't fun anymore, and I don't really want to start counting the sphincters doors in my body.

I clearly misread the room because we all seem to be hell bent on forcing this overly loose interpretation so that everything counts as a wheel for the meme.