The foldings of a square to convex polyhedra

Abstract

The structure of the set of all convex polyhedra foldable from a square is detailed. It is proved that five combinatorially distinct nondegenerate polyhedra, and four different flat polyhedra, are realizable. All the polyhedra are continuously deformable into each other, with the space of polyhedra having the topology of four connected rings. © Springer-Verlag Berlin Heidelberg 2003.