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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2015, Volume 289, Pages 115–144
DOI: https://doi.org/10.1134/S0371968515020077 (Mi tm3624) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Truncations of simple polytopes and applications

V. M. Buchstabera, N. Yu. Erokhovetsb

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b Lomonosov Moscow State University, Moscow, Russia
Full-text PDF (386 kB) Citations (16)
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DOI: https://doi.org/10.1134/S0371968515020077
Abstract: We introduce and analyze truncation operations on simple polytopes. The results obtained allow us to describe relations between various classes of polytopes. Special attention is paid to three-dimensional polytopes and, first of all, fullerenes.
Funding agency Grant number
Russian Science Foundation 14-11-00414
This work is supported by the Russian Science Foundation under grant 14-11-00414.
Received: March 15, 2015
English version:
Proceedings of the Steklov Institute of Mathematics, 2015, Volume 289, Pages 104–133
DOI: https://doi.org/10.1134/S0081543815040070
Bibliographic databases:
Document Type: Article
UDC: 514.172.45
Language: Russian
Citation: V. M. Buchstaber, N. Yu. Erokhovets, “Truncations of simple polytopes and applications”, Selected issues of mathematics and mechanics, Collected papers. In commemoration of the 150th anniversary of Academician Vladimir Andreevich Steklov, Trudy Mat. Inst. Steklova, 289, MAIK Nauka/Interperiodica, Moscow, 2015, 115–144; Proc. Steklov Inst. Math., 289 (2015), 104–133
Citation in format AMSBIB
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\paper Truncations of simple polytopes and applications
\inbook Selected issues of mathematics and mechanics
\bookinfo Collected papers. In commemoration of the 150th anniversary of Academician Vladimir Andreevich Steklov
\serial Trudy Mat. Inst. Steklova
\yr 2015
\vol 289
\pages 115--144
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3624}
\crossref{https://doi.org/10.1134/S0371968515020077}
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Linking options:
  • https://www.mathnet.ru/eng/tm3624
  • https://doi.org/10.1134/S0371968515020077
  • https://www.mathnet.ru/eng/tm/v289/p115
    • This publication is cited in the following 16 articles:
    1. N. M. Adrianov, G. B. Shabat, “Fullereny i funktsii Belogo”, Fundament. i prikl. matem., 25:2 (2024), 41–61  mathnet
    2. Nikolai Yu. Erokhovets, “Cohomological Rigidity of Families of Manifolds Associated with Ideal Right-Angled Hyperbolic 3-Polytopes”, Proc. Steklov Inst. Math., 318 (2022), 90–125  mathnet  crossref  crossref  mathscinet
    3. N. Yu. Erokhovets, “Theory of families of polytopes: fullerenes and Pogorelov polytopes”, Moscow University Mathematics Bulletin, 76:2 (2021), 83–95  mathnet  crossref  mathscinet  zmath  isi
    4. Piotr Beben, Jelena Grbić, “LS-category of moment-angle manifolds and higher order Massey products”, Forum Mathematicum, 33:5 (2021), 1179  crossref
    5. D. Baralic, J. Grbic, I. Limonchenko, A. Vucic, “Toric objects associated with the dodecahedron”, Filomat, 34:7 (2020), 2329–2356  crossref  mathscinet  isi
    6. N. Yu. Erokhovets, “Three-Dimensional Right-Angled Polytopes of Finite Volume in the Lobachevsky Space: Combinatorics and Constructions”, Proc. Steklov Inst. Math., 305 (2019), 78–134  mathnet  crossref  crossref  mathscinet  isi  elib
    7. N. Erokhovets, “Construction of fullerenes and Pogorelov polytopes with 5-, 6-and one 7-gonal face”, Symmetry-Basel, 10:3 (2018), 67, 28 pp.  crossref  mathscinet  isi
    8. V. M. Buchstaber, N. Yu. Erokhovets, “Fullerenes, polytopes and toric topology”, Combinatorial and Toric Homotopy: Introductory Lectures, Lecture Notes Series Institute For Mathematical Sciences National University of Singapore, 35, eds. A. Darby, J. Grbic, Z. Lu, J. Wu, World Scientific Publ Co Pte Ltd, 2018, 67–178  crossref  mathscinet  isi
    9. E. S. Karpova, A. V. Timofeenko, “O razbieniyakh usechennogo ikosaedra na parketogranniki”, Chebyshevskii sb., 19:2 (2018), 447–476  mathnet  crossref  elib
    10. V. M. Buchstaber, N. Yu. Erokhovets, M. Masuda, T. E. Panov, S. Park, “Cohomological rigidity of manifolds defined by 3-dimensional polytopes”, Russian Math. Surveys, 72:2 (2017), 199–256  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. A. Yu. Vesnin, “Right-angled polyhedra and hyperbolic 3-manifolds”, Russian Math. Surveys, 72:2 (2017), 335–374  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. V. M. Buchstaber, N. Yu. Erokhovets, “Finite sets of operations sufficient to construct any fullerene from $C_{20}$”, Struct. Chem., 28:1, SI (2017), 225–234  crossref  mathscinet  isi  scopus
    13. V. M. Buchstaber, N. Yu. Erokhovets, “Constructions of families of three-dimensional polytopes, characteristic patches of fullerenes, and Pogorelov polytopes”, Izv. Math., 81:5 (2017), 901–972  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    14. 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
    15. N. Yu. Erokhovets, “$k$-poyasa i rebernye tsikly trekhmernykh prostykh mnogogrannikov s ne bolee chem shestiugolnymi granyami”, Dalnevost. matem. zhurn., 15:2 (2015), 197–213  mathnet  elib
    16. N. V. Prudnikova, “Konstruktsii fullerenov s chislom shestiugolnikov ne bolshe 7”, Dalnevost. matem. zhurn., 15:2 (2015), 247–263  mathnet  elib
    Citing articles in Google Scholar: Russian citations, English citations
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