For a polyhedron Q, a polygon obtained by cutting the edges or faces of Q is called a general unfolding. A general unfolding may have a self-overlap or self-intersection on the boundary which depends on the way of unfolding. It is established by Aronov and O’Rourke and Sharir and Schorr that any convex polyhedron satisfies the property that at least one general unfolding has no overlap. This research focuses on a dual property in which any general unfolding has no overlap, called overlap-free. We show that a polyhedron is overlap-free if and only if it is a stamper, which is a notion introduced by Akiyama. This means that if a polyhedron is not a stamper, at least one general unfolding has an overlap. We prove it in a constructive way.