Flexible cross-polytopes in spaces of constant curvature

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We construct self-intersecting flexible cross-polytopes in the spaces of constant curvature, that is, in Euclidean spaces En, spheres Sn, and Lobachevsky spaces Λn of all dimensions n. In dimensions n ≥ 5, these are the first examples of flexible polyhedra. Moreover, we classify all flexible cross-polytopes in each of the spaces En, Sn, and Λn. For each type of flexible cross-polytopes, we provide an explicit parametrization of the flexion by either rational or elliptic functions.

Original languageEnglish
Pages (from-to)77-113
Number of pages37
JournalProceedings of the Steklov Institute of Mathematics
Issue number1
Publication statusPublished - 1 Oct 2014


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