I have two convex polyhedra such that their sums of side areas are equal. It is true that I can cut one of them and flatten it on the plane, then fold the flattened polygon to reach the other polyhedron?

For special case in which these two polyhedra are cube and regular tetrahedron, The answer in Yes I think. But I think the answer is "No, not necessarily" in general case, and I think the problem is difficult!