Nonrigid star-like bipyramids of A. D. Alexandrov and S. M. Vladimirova (Q1876362)

The author establishes the existence of nonrigid polyhedra with stationary volume. He shows that a one-parameter family of such polyhedra (considered up to homothety) lies in the class of starlike bipyramids. He proves that those starlike bipyramids are second-order rigid, finds so-called model flexors among starlike bipyramids, and reveals fractal and dynamical properties of invariant functions of this class of polyhedra. This is an English translation of the author's article published in the book [\textit{S. K. Vodop'yanov (ed.), Proceedings on Analysis and Geometry. International conference in honor of the 70th birthday of Professor Yu. G. Reshetnyak. Novosibirsk: Izdatel'stvo Instituta Matematiki, 414--420 (2000; Zbl 0990.52002)].}