If the coin is perfectly circular, is does in fact have only 2 sides (as a perfect circle has no sides).
If the coin is not perfectly circular, but is (at some microscopic level) full of edges, it could have a near infinite amount of sides.
A perfectly cylindrical coin would have three sides: 2 flat planes and a curved ribbon. No reason a “side” has to be flat. Just ain’t got no internal edges!
Depends on whether a "side" is an "edge" of a "face" in geometry terms. An edge must be two-dimensional (so flat), a face can be three-dimensional (like a curved ribbon).
