If these properties hold for a given mesh, is the mesh guaranteed to be manifold?
I don't think so! From my understanding, these properties are the result of a 2D mesh having edges that line up. I did some more reading about manifolds and the Euler's formula, and every definition / description uses "if" logic instead of "if and only if". I know this isn't a satisfying answer, and I can't find an actual counter-example, so would also love some guidance on this!
Is it possible for an edge to connect more than two vertices? An edge is basically a line between two vertices, right?