That makes sense, I didn't realize we were allowed to stretch and bend however we want. Seems weird to be allowed to take a 3D object and contort it into 2D.
But it is not a 3D object, it is in fact a 2D object embedded in the 3D space. (So, what you are looking at is the result of an arbitrary “projection” of one into the other - a map, in mathematical terms.)
If you want to consider a more restrictive collection of modifications, like, say you want to preserve angles or something inside the shape, then that would be a different question. Uh, I guess if you had a surface which was generally smooth but possibly has some boundaries and/or corner edge things, and/or corner point things (e.g. sticking two cones together), you could also ask about how many cuts combined with conformal maps [edit : I think conformal maps isn't the thing I'm looking for. Yeah, I think I'm looking for something related to developable surfaces maybe] would be needed to flatten such a thing out? (so this could maybe produce a similar question for which the one or half or whatever cut between the edge of the cone and the center, could be an answer?)