ABSTRACT
It is a long-standing open problem to determine whether every convex polyhedron can be cut along its edges and unfolded flat in one piece without overlap, that is, into a simple polygon. This type of unfolding has been termed an edge-unfolding; the unfolding consists of the facets of the polyhedron joined along edges. In contrast, unfolding via arbitrary cuts easily leads to non-overlap. See [11] for a history of the edge-unfolding problem and its applications to manufacturing. Recently it was established that not every nonconvex polyhedron can be edge-unfolded, even if the polyhedron is simplicial, that is, all of its faces are triangles [2, 3].
