A starshaped polyhedron with no net (Q2765091)

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scientific article; zbMATH DE number 1693695
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A starshaped polyhedron with no net
scientific article; zbMATH DE number 1693695

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    19 November 2002
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    nets of polyhedra
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    A starshaped polyhedron with no net (English)
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    A net of a polyhedron \(P\) is a simple plane polygon subdivided without overlaps into polygons, congruent to the faces of \(P\). At the present time there is only a conjecture that every convex polyhedron has a net. The analogous question for nonconvex polyhedra has been answered in the negative by \textit{A. S. Tarasov} [Russ. Math. Surv. 54, No. 3, 656-657 (1999); translation from Usp. Mat. Nauk 54, No. 3, 185-186 (1999; Zbl 0968.52007)]. The author gives a simple construction for a starshaped polyhedron which establishes the following result: There exist nonconvex polyhedral spheres without nets.
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