Existence of a polyhedron which does not have a non-overlapping pseudo-edge unfolding

Abstract

There exists a surface of a convex polyhedron P and a partition L of P into geodesic convex polygons such that there are no connected "edge" unfoldings of P without self-intersections (whose spanning tree is a subset of the edge skeleton of L).

24 pages, 20 figuers, minor grammatical changes