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Izvestiya: Mathematics, 2017, Volume 81, Issue 5, Pages 901–972
DOI: https://doi.org/10.1070/IM8665 (Mi im8665) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Constructions of families of three-dimensional polytopes, characteristic patches of fullerenes, and Pogorelov polytopes

V. M. Buchstaber, N. Yu. Erokhovets

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
English version PDF (1222 kB) Citations (15)
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DOI: https://doi.org/10.1070/IM8665
Abstract: We describe the combinatorics of three families of simple 3-dimensional polytopes which play an important role in various problems of algebraic topology, hyperbolic geometry, graph theory, and their applications. The first family $\mathcal{P}_{\leqslant 6}$ consists of simple polytopes with at most hexagonal faces. The second family $\mathcal{P}_\mathrm{pog}$ consists of Pogorelov polytopes. The third family $\mathcal{F}$ consists of fullerenes and is the intersection of the first two. We show that in the case of fullerenes there are stronger results than for the first two. Our main tools are $k$-belts of faces, simple partitions of a disc and the operations of transformation and connected sum.
Keywords: fullerene, nanotube, Pogorelov polytope, partition of a disc, operations of cutting off edges, operations of connected sum and addition of a belt, patches, $k$-belts.
Funding agency Grant number
Russian Science Foundation 14-11-00414
This work is supported by the Russian Science Foundation under grant no. 14-11-00414.
Received: 14.02.2017
Revised: 15.04.2017
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2017, Volume 81, Issue 5, Pages 15–91
DOI: https://doi.org/10.4213/im8665
Bibliographic databases:
Document Type: Article
UDC: 514.172.45
MSC: 05C75, 52B10, 92E10
Language: English
Original paper language: Russian
Citation: V. M. Buchstaber, N. Yu. Erokhovets, “Constructions of families of three-dimensional polytopes, characteristic patches of fullerenes, and Pogorelov polytopes”, Izv. RAN. Ser. Mat., 81:5 (2017), 15–91; Izv. Math., 81:5 (2017), 901–972
Citation in format AMSBIB
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:228
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    References:50
    First page:37
     
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