Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2021, Number 2, Pages 61–72 (Mi vmumm4396)  

This article is cited in 1 scientific paper (total in 1 paper)

Award I. I. Shuvalov

Theory of families of polytopes: fullerenes and Pogorelov polytopes

N. Yu. Erokhovets

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (522 kB) Citations (1)
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Abstract: The paper is a review of the results of the eponymous cycle of author's works marked by the I. I. Shuvalov I degree prize 2018 for scientific research and recent results. We study families of three-dimensional simple polytopes defined by the condition of cyclic $k$-edge-connectivity, in particular, flag polytopes and Pogorelov polytopes, as well as related families of fullerenes and ideal right-angled hyperbolic polytopes. We describe methods for constructing families using operations of cutting off edges and a connected sum along faces, a construction of fullerenes using growth operations, a construction of cohomologically rigid families of three-dimensional and six-dimensional manifolds, and Thurston's geometrization of orientable three-dimensional manifolds corresponding to polytopes.
Key words: three-dimensional polytope, cyclic $k$-edge-connectivity, family of polytopes, fullerene, right-angled polytope, hyperbolic manifold, cohomological rigidity, geometrization.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00675
Received: 26.02.2020
English version:
Moscow University Mathematics Bulletin, 2021, Volume 76, Issue 2, Pages 83–95
DOI: https://doi.org/10.3103/S0027132221020042
Bibliographic databases:
Document Type: Article
UDC: 514.172.45+514.132+515.14+515.16+519.17
Language: Russian
Citation: N. Yu. Erokhovets, “Theory of families of polytopes: fullerenes and Pogorelov polytopes”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2021, no. 2, 61–72; Moscow University Mathematics Bulletin, 76:2 (2021), 83–95
Citation in format AMSBIB
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\jour Moscow University Mathematics Bulletin
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:27
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