Article ID Journal Published Year Pages File Type
414830 Computational Geometry 2008 13 Pages PDF
Abstract

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.

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Physical Sciences and Engineering Computer Science Computational Theory and Mathematics