Ukrainian Mathematical Journal

, Volume 70, Issue 7, pp 1022–1041 | Cite as

Birosettes Are Model Flexors

  • V. A. Gor’kavyi
  • A. D. Milka

A new family of polyhedra called birosettes is presented. The geometric features of birosettes are analyzed. The model flexibility of birosettes is explained.


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  1. 1.
    M. Berger, Géométrie, Nathan, Paris (1977).zbMATHGoogle Scholar
  2. 2.
    A. D. Aleksandrov, Convex Polyhedra [in Russian], Gostekhizdat, Moscow (1950).Google Scholar
  3. 3.
    A. D. Milka, “Linear bendings of convex polyhedra,” Mat. Fiz., Analiz, Geometr., 1, 116–130 (1994).MathSciNetzbMATHGoogle Scholar
  4. 4.
    A. D. Milka, “Linear bendings of regular convex polyhedra,” in: Abstr. of Short Communications and Poster Sessions at the Internat. Congr. of Mathematicians (Berlin, August 18–27, 1998), Berlin (1998).Google Scholar
  5. 5.
    A. D. Milka, “Nonrigid starlike Aleksandrov and Vladimirova bipyramids,” in: Proceedings in Analysis and Geometry [in Russian], Institute of Mathematics, Novosibirsk (2000), pp. 414–430.Google Scholar
  6. 6.
    A. D. Milka, “Bendings of the surfaces, bifurcations of dynamical systems, and stability of shells,” in: Chebyshev Collection [in Russian], 7, (2006), pp. 109–144.Google Scholar
  7. 7.
    A. D. Milka, “Linear bendings of starlike bipyramids,” Proc. Internat. Geom. Center., 1, No. 1-2, 71–96 (2008).Google Scholar
  8. 8.
    A. Douady, “Le shaddock á six becs,” Bull. A. P. M. E. P., 281, 699 (1971).Google Scholar
  9. 9.
    R. Connelly, “A counterexample to the rigidity conjecture for polyhedra,” Publ. Math. l’IHES, 47, 333–338 (1977).MathSciNetCrossRefGoogle Scholar
  10. 10.
    P. R. Cromwell, Polyhedra, Cambridge Univ. Press, Cambridge (1999).zbMATHGoogle Scholar
  11. 11.
    D. Fuchs and S. Tabachnikov, Mathematical Omnibus: Thirty Lectures on Classic Mathematics, American Mathematical Society, Providence, RI (2007).CrossRefGoogle Scholar
  12. 12.
    V. Gorkavyy and D. Kalinin, “On model flexibility of the Jessen orthogonal icosahedron,” Contrib. Algebra Geom., 57, No. 3, 607–622 (2016).MathSciNetCrossRefGoogle Scholar
  13. 13.
    A. D. Milka, “Linear bending of starlike pyramids,” C. R. Mec., 331, No. 12, 805–810 (2003).CrossRefGoogle Scholar
  14. 14.
    A. V. Pogorelov, Bendings of the Surfaces and Stability of Shells, American Mathematical Society, Providence, RI (1988).Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • V. A. Gor’kavyi
    • 1
  • A. D. Milka
    • 1
  1. 1.Verkin Institute for Low Temperature Physics and EngineeringUkrainian National Academy of SciencesKharkovUkraine

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