A cone surface is topologically equivalent to a disk. You don't have to cut it at all in order to flatten it, if you allow as much stretching and bending as you

A cone surface is topologically equivalent to a disk. You don't have to cut it at all in order to flatten it, if you allow as much stretching and bending as you want. So, 0 holes. 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?)