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.
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Alexander, R., Dyson, H., O’Rourke, J. (2003). The Foldings of a Square to Convex Polyhedra. In: Akiyama, J., Kano, M. (eds) Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol 2866. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44400-8_5
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DOI: https://doi.org/10.1007/978-3-540-44400-8_5
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