On the Fewest Nets Problem for Convex Polyhedra

Given a convex polyhedron with n vertices and F faces, what is the fewest number of pieces, each of which unfolds to a simple polygon, into which it may be cut by slices along edges? Shephard’s conjecture says that this number is always 1, but it’s still open. The fewest nets problem asks to provide upper bounds for the number of pieces in terms of n and/or F. We improve the previous best known bound of F/2 by proving that every convex polyhedron can be unfolded into no more than 3F/8 non-overlapping nets. If the polyhedron is triangulated,

• Type: Conference
• Year: 2007
• Where: CCCG
• Authors: Val Pinciu
• Keywords: CCCG 2007, Computational Geometry, Convex Polyhedron, Fewest Nets, Fewest Number