Abstract. We extend the notion of a source unfolding of a convex polyhedron P to be based on a closed polygonal curve Q in a particular class rather than based on a point. The class requires that Q “lives on a cone” to both sides; it includes simple, closed quasigeodesics. Cutting a particular subset of the cut locus of Q (in P) leads to a non-overlapping unfolding of the polyhedron. This gives a new general method to unfold the surface of any convex polyhedron to a simple, planar polygon
Itoh, Jin-ichi; O'Rourke, Joseph; and Vîlcu, Costin, "Source Unfoldings of Convex Polyhedra via Certain Closed Curves" (2012). Faculty Publications. Paper 20.