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.
|Number of pages||37|
|Journal||Proceedings of the Steklov Institute of Mathematics|
|Publication status||Published - 1 Oct 2014|