A method for the characterization of foldings in protein ribbon models
Journal of Molecular Graphics
On the development of the intersection of a plane with a polytope
Computational Geometry: Theory and Applications - Special issue on Discrete and computational geometry
Folding and Unfolding in Computational Geometry
JCDCG '98 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
An Extension of Cauchy's Arm Lemma with Application to Curve Development
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Reconfigurations of polygonal structures
Reconfigurations of polygonal structures
Geometric Folding Algorithms: Linkages, Origami, Polyhedra
Geometric Folding Algorithms: Linkages, Origami, Polyhedra
Development of curves on polyhedra via conical existence
Computational Geometry: Theory and Applications
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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.