Computational Geometry: Theory and Applications
A band is the intersection of the surface of a convex polyhedron with the space between two parallel planes, as long as this space does not contain any vertices of the polyhedron. The intersection of the planes and the polyhedron produces two convex polygons. If one of these polygons contains the other in the projection orthogonal to the parallel planes, then the band is nested. We prove that all nested bands can be unfolded, by cutting along exactly one edge and folding continuously to place all faces of the band into a plane, without intersection. © 2007 Elsevier B.V.
Folding, Polyhedra, Slice curves
© the authors
Aloupis, Greg; Demaine, Erik D.; Langerman, Stefan; Morin, Pat; O'Rourke, Joseph; Streinu, Ileana; and Toussaint, Godfried, "Edge-Unfolding Nested Polyhedral Bands" (2008). Computer Science: Faculty Publications, Smith College, Northampton, MA.