Title: Pseudo-edge unfoldings of convex polyhedra,
Abstract: A pseudo-edge graph of a convex polyhedron K is a 3-connected embedded graph
in K whose vertices coincide with those of K, whose edges are distance
minimizing geodesics, and whose faces are convex. We construct a convex
polyhedron K in Euclidean 3-space with a pseudo-edge graph E with respect to
which K is not unfoldable. The proof is based on a result of Pogorelov on
convex caps with prescribed curvature, and an unfoldability criterion for
almost flat convex caps due to Tarasov. Our example, which has 340 vertices,
significantly simplifies an earlier construction by Tarasov, and confirms that
Durer's conjecture does not hold for pseudo-edge unfoldings.