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Tr. Mat. Inst. Steklova, 2015, Volume 288, Pages 171–183 (Mi tm3592)  

This article is cited in 3 scientific papers (total in 3 papers)

On flexible polyhedral surfaces

M. I. Shtogrin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: We construct a closed orientable polyhedral surface of arbitrary genus that is embedded in three-dimensional Euclidean space and admits a one-parameter bending under which all its handles bend. This surface admits no other bendings. We also construct a flexible closed nonorientable polyhedral surface of arbitrary genus such that all its handles and Möbius strips bend during its bending.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.1134/S0371968515010124

Full text: PDF file (199 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 288, 153–164

Bibliographic databases:

UDC: 514.752.43
Received in January 2015

Citation: M. I. Shtogrin, “On flexible polyhedral surfaces”, Geometry, topology, and applications, Collected papers. Dedicated to Professor Nikolai Petrovich Dolbilin on the occasion of his 70th birthday, Tr. Mat. Inst. Steklova, 288, MAIK Nauka/Interperiodica, Moscow, 2015, 171–183; Proc. Steklov Inst. Math., 288 (2015), 153–164

Citation in format AMSBIB
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\by M.~I.~Shtogrin
\paper On flexible polyhedral surfaces
\inbook Geometry, topology, and applications
\bookinfo Collected papers. Dedicated to Professor Nikolai Petrovich Dolbilin on the occasion of his 70th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2015
\vol 288
\pages 171--183
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3592}
\crossref{https://doi.org/10.1134/S0371968515010124}
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\jour Proc. Steklov Inst. Math.
\yr 2015
\vol 288
\pages 153--164
\crossref{https://doi.org/10.1134/S0081543815010125}
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  • https://doi.org/10.1134/S0371968515010124
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. Kh. Sabitov, “The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research”, Trans. Moscow Math. Soc., 77 (2016), 149–175  mathnet  crossref  elib
    2. D. I. Sabitov, I. Kh. Sabitov, “Mnogochleny ob'ema dlya mnogogrannikov kombinatornogo tipa $n$-grannykh prizm v sluchayakh $n=5,6,7$”, Sib. elektron. matem. izv., 16 (2019), 439–448  mathnet  crossref
    3. Alexandrov V., “A Sufficient Condition For a Polyhedron to Be Rigid”, J. Geom., 110:2 (2019), UNSP 38  crossref  isi
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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