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Open AccessArticle

Enumeration of Pentahexagonal Annuli in the Plane

1
Laboratory of Topology and Dynamics, Novosibirsk State University, Novosibirsk 630090, Russia
2
Laboratory of Graph Theory, Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russia
3
Department of Computer Science and Mathematics, Ariel University, Ariel 4070000, Israel
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1156; https://doi.org/10.3390/math7121156
Received: 18 October 2019 / Revised: 11 November 2019 / Accepted: 22 November 2019 / Published: 1 December 2019
(This article belongs to the Special Issue Graph Theory at Work in Carbon Chemistry)
Pentahexagonal annuli are closed chains consisting of regular pentagons and hexagons. Such configurations can be easily recognized in various complex designs, in particular, in molecular carbon constructions. Results of computer enumeration of annuli without overlapping on the plane are presented for up to 18 pentagons and hexagons. We determine how many annuli have certain properties for a fixed number of pentagons. In particular, we consider symmetry, pentagon separation (the least ring-distance between pentagons), uniformity of pentagon distribution, and pentagonal thickness (the size of maximal connected part of pentagons) of annuli. Pictures of all annuli with the number of pentagons and hexagons up to 17 are presented (more than 1300 diagrams). View Full-Text
Keywords: pentahexagonal annuli; constructive enumeration; nanoarchitecture pentahexagonal annuli; constructive enumeration; nanoarchitecture
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Dobrynin, A.A.; Rosenfeld, V.R. Enumeration of Pentahexagonal Annuli in the Plane. Mathematics 2019, 7, 1156.

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