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Tr. Mat. Inst. Steklova, 2015, Volume 289, Pages 115–144 (Mi tm3624)  

This article is cited in 11 scientific papers (total in 11 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

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.


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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 289, 104–133

Bibliographic databases:

UDC: 514.172.45
Received: March 15, 2015

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, Tr. Mat. Inst. Steklova, 289, MAIK Nauka/Interperiodica, Moscow, 2015, 115–144; Proc. Steklov Inst. Math., 289 (2015), 104–133

Citation in format AMSBIB
\by V.~M.~Buchstaber, N.~Yu.~Erokhovets
\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 Tr. Mat. Inst. Steklova
\yr 2015
\vol 289
\pages 115--144
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\jour Proc. Steklov Inst. Math.
\yr 2015
\vol 289
\pages 104--133

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    This publication is cited in the following articles:
    1. 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
    2. N. V. Prudnikova, “Konstruktsii fullerenov s chislom shestiugolnikov ne bolshe 7”, Dalnevost. matem. zhurn., 15:2 (2015), 247–263  mathnet  elib
    3. 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
    4. 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  adsnasa  isi  elib
    5. A. Yu. Vesnin, “Right-angled polyhedra and hyperbolic 3-manifolds”, Russian Math. Surveys, 72:2 (2017), 335–374  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. 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  isi  scopus
    7. 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  adsnasa  isi  elib
    8. 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  isi
    9. 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  isi
    10. E. S. Karpova, A. V. Timofeenko, “O razbieniyakh usechennogo ikosaedra na parketogranniki”, Chebyshevskii sb., 19:2 (2018), 447–476  mathnet  crossref  elib
    11. 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  isi  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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