Development of Curves on Polyhedra Via Conical Existence
Abstract
We establish that certain classes of simple, closed, polygonal curves on the surface of a convex polyhedron develop in the plane without overlap. Our primary proof technique shows that such curves "live on a cone," and then develops the curves by cutting the cone along a "generator" and attening the cone in the plane. The conical existence results support a type of source unfold- ing of the surface of a polyhedron, described elsewhere.
This paper has been withdrawn.