We establish that certain classes of simple, closed, polygonal curves on the surface of a convex polyhedron develop in the plane without overlap.

Aug 12, 2011 · We establish that certain classes of simple, closed, polygonal curves on the surface of a convex polyhedron develop in the plane without ...

Abstract. We establish that certain classes of simple, closed, polygonal curves on the surface of a convex polyhedron develop in the plane without overlap.

Feb 1, 2014 · 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 ...

We establish that certain classes of simple, closed, polygonal curves on the surface of a convex polyhedron develop in the plane without overlap.

Development of curves on polyhedra via conical existence. ✩. Joseph O'Rourke ... polyhedra via certain closed curves, 2011, submitted for publication.

We establish that certain classes of simple, closed, polygonal curves on the surface of a convex polyhedron develop in the plane without overlap.

It is shown that a closed convex polygonal curve on the surface of a 3-polytope develops in the plane to a simple path: it does not self-intersect.

Feb 4, 2011 · We identify several classes of curves C that "live on a cone," in the sense that C and a neighborhood to one side may be isometrically embedded ...

Development of curves on polyhedra via conical existence · Joseph O'Rourke. 2014, Computational Geometry ; Inscribed and Circumscribed Circles to Convex Curves.