Can a convex polyhedron have a developable face-cycle?

A face-cycle of a polyhedron in R-3 is a cyclic sequence of at least three, distinct faces of the polyhedron such that each consecutive pair of faces have a common edge. We prove that for any face-cycle cut out from a (cardbo ard) convex polyhedron, it is impossible to unfold the face-cycle to lie fl at on the plane. (C) 2000 Elsevier Science B.V. All rights reserved.