Enumeration of Pentahexagonal Annuli in the Plane

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Enumeration of Pentahexagonal Annuli in the Plane. / Dobrynin, Andrey A.; Rosenfeld, Vladimir R.

In: Mathematics, Vol. 7, No. 12, 1156, 01.12.2019.

Research output: Contribution to journal › Article › peer-review

Harvard

Dobrynin, AA & Rosenfeld, VR 2019, 'Enumeration of Pentahexagonal Annuli in the Plane', Mathematics, vol. 7, no. 12, 1156. https://doi.org/10.3390/math7121156

APA

Dobrynin, A. A., & Rosenfeld, V. R. (2019). Enumeration of Pentahexagonal Annuli in the Plane. Mathematics, 7(12), [1156]. https://doi.org/10.3390/math7121156

Vancouver

Dobrynin AA, Rosenfeld VR. Enumeration of Pentahexagonal Annuli in the Plane. Mathematics. 2019 Dec 1;7(12):1156. doi: 10.3390/math7121156

Author

Dobrynin, Andrey A. ; Rosenfeld, Vladimir R. / Enumeration of Pentahexagonal Annuli in the Plane. In: Mathematics. 2019 ; Vol. 7, No. 12.

BibTeX

@article{1947da77603b4cbe8a2d793501889643,

title = "Enumeration of Pentahexagonal Annuli in the Plane",

abstract = "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).",

keywords = "pentahexagonal annuli, constructive enumeration, nanoarchitecture, LIQUID-CRYSTALS, FULLERENES, GENERATION, GRAPHS, SYMMETRY, CHAINS, RULE, Constructive enumeration, Nanoarchitecture, Pentahexagonal annuli",

author = "Dobrynin, {Andrey A.} and Rosenfeld, {Vladimir R.}",

note = "Publisher Copyright: {\textcopyright} 2019 by the authors.",

year = "2019",

month = dec,

day = "1",

doi = "10.3390/math7121156",

language = "English",

volume = "7",

journal = "Mathematics",

issn = "2227-7390",

publisher = "MDPI AG",

number = "12",

}

RIS

TY - JOUR

T1 - Enumeration of Pentahexagonal Annuli in the Plane

AU - Dobrynin, Andrey A.

AU - Rosenfeld, Vladimir R.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - 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).

AB - 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).

KW - pentahexagonal annuli

KW - constructive enumeration

KW - nanoarchitecture

KW - LIQUID-CRYSTALS

KW - FULLERENES

KW - GENERATION

KW - GRAPHS

KW - SYMMETRY

KW - CHAINS

KW - RULE

KW - Constructive enumeration

KW - Nanoarchitecture

KW - Pentahexagonal annuli

UR - http://www.scopus.com/inward/record.url?scp=85079686943&partnerID=8YFLogxK

U2 - 10.3390/math7121156

DO - 10.3390/math7121156

M3 - Article

VL - 7

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 12

M1 - 1156

ER -

ID: 23288284