To my Advisor Victor Matveevich Buchstaber on the occasion of his seventieth birthday
Abstract
We construct self-intersecting flexible cross-polytopes in the spaces of constant curvature, that is, in Euclidean spaces \(\mathbb{E}^n\), spheres \(\mathbb{S}^n\), 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 \(\mathbb{E}^n\), \(\mathbb{S}^n\), and Λn. For each type of flexible cross-polytopes, we provide an explicit parametrization of the flexion by either rational or elliptic functions.
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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Vol. 286, pp. 88–128.
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Gaifullin, A.A. Flexible cross-polytopes in spaces of constant curvature. Proc. Steklov Inst. Math. 286, 77–113 (2014). https://doi.org/10.1134/S0081543814060066
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DOI: https://doi.org/10.1134/S0081543814060066