| Unfolding Some Classes of Orthogonal Polyhedra (1998) | |||||||||||||||
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| In this paper, we study unfoldings of orthogonal polyhedra. More precisely, we define two special classes of orthogonal polyhedra, orthostacks and orthotubes, and show how to generate unfoldings by cutting faces, such that the resulting surfaces can be flattened into a single connected polygon. 1 Introduction An unfolding of a polyhedron is a cutting of the polyhedron's surface so that the surface can be flattened into a single simple polygon that does not overlap itself. Finding unfoldings is a classic problem. Not only does it have connections with origami, but it also has potential industrial applications, because an unfolding allows one to construct a desired physical shape by folding and gluing a polygonal cut-out of a stiff sheet of material. Unfoldings can be classified by whether all cuts are along edges of the polyhedron (edge cuts), or whether cuts across faces are allowed as well. It is an open problem to determine whether every convex polyhedron has an unfolding with only... | |||||||||||||||
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