Symmetry 2018, 10(3), 67; doi:10.3390/sym10030067
Construction of Fullerenes and Pogorelov Polytopes with 5-, 6- and one 7-Gonal Face
Steklov Mathematical Institute of Russian Academy of Sciences, 119991 Moscow, Russia
†
The author is a Young Russian Mathematics award winner.
Received: 19 January 2018 / Revised: 7 March 2018 / Accepted: 9 March 2018 / Published: 15 March 2018
(This article belongs to the Special Issue Mathematical Crystallography)
Abstract
A Pogorelov polytope is a combinatorial simple 3-polytope realizable in the Lobachevsky (hyperbolic) space as a bounded right-angled polytope. These polytopes are exactly simple 3-polytopes with cyclically 5-edge connected graphs. A Pogorelov polytope has no 3- and 4-gons and may have any prescribed numbers of k-gons,Keywords:
fullerenes; right-angled polytopes; truncation of edges; connected sum; k-belts; p-vector; cyclically 5-edge connected graph
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Erokhovets, N. Construction of Fullerenes and Pogorelov Polytopes with 5-, 6- and one 7-Gonal Face. Symmetry 2018, 10, 67.
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