We extend the notion of a star unfolding to be based on a simple quasigeodesic loop Q rather than on a point. This gives a new general method to unfold the surface of any convex polyhedron P to a simple, planar polygon: shortest paths from all vertices of P to Q are cut, and all but one segment of Q is cut.
Itoh, Jin-ichi; O'Rourke, Joseph; and Vîlcu, Costin, "Unfolding Convex Polyhedra via Quasigeodesic Star Unfoldings" (2008). Faculty Publications. Paper 39.