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Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2021, Number 2, Pages 61–72 (Mi vmumm4396)  

Award I. I. Shuvalov

Theory of families of polytopes: fullerenes and polytopes of A.V. Pogorelov

N. Yu. Erokhovets

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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


Full text: PDF file (522 kB)
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UDC: 514.172.45+514.132+515.14+515.16+519.17
Received: 26.02.2020

Citation: N. Yu. Erokhovets, “Theory of families of polytopes: fullerenes and polytopes of A.V. Pogorelov”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2021, no. 2, 61–72

Citation in format AMSBIB
\Bibitem{Ero21}
\by N.~Yu.~Erokhovets
\paper Theory of families of polytopes: fullerenes and polytopes of A.V. Pogorelov
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2021
\issue 2
\pages 61--72
\mathnet{http://mi.mathnet.ru/vmumm4396}


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