Continuous Flattening of Convex Polyhedra
A flat folding of a polyhedron is a folding by creases into a multilayered planar shape. It is an open problem of E. Demaine et al., that every flat folded state of a polyhedron can be reached by a continuous folding process. Here we prove that every convex polyhedron possesses infinitely many continuous flat folding processes. Moreover, we give a sufficient condition under which every flat folded state of a convex polyhedron can be reached by a continuous folding process.
KeywordsConvex Polyhedron Folding Process Polyhedral Surface Leaf Edge Original Face
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