Re: [math-fun] Unfolding questions

<< Is there a convex polyhedron for which some unfolding exhibits overlapping faces in the plane? >>

Intuitively, `unfolding' can only increase the distance between (given points on) any two faces. However, it's not at the moment obvious to me exactly why this should be a consequence of convexity ...

If you swap the existential quantifier with a universal one, you get an unsolved problem: "Does every convex polyhedron have at least one net (unfolding without overlaps)?" ...so I imagine that, for this to be unsolved, there must be convex polyhedra for which there is at least one unfolding with overlaps. Best wishes, Adam P. Goucher