Schwarzite nets: a wealth of 3-valent examples sharing similar topologies and symmetries

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Schwarzite nets : a wealth of 3-valent examples sharing similar topologies and symmetries. / Hyde, Stephen T.; Pedersen, Martin Cramer.

In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 477, No. 2246, 20200372, 03.02.2021.

Research output: Contribution to journalJournal articleResearchpeer-review

Harvard

Hyde, ST & Pedersen, MC 2021, 'Schwarzite nets: a wealth of 3-valent examples sharing similar topologies and symmetries', Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 477, no. 2246, 20200372. https://doi.org/10.1098/rspa.2020.0372

APA

Hyde, S. T., & Pedersen, M. C. (2021). Schwarzite nets: a wealth of 3-valent examples sharing similar topologies and symmetries. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 477(2246), [20200372]. https://doi.org/10.1098/rspa.2020.0372

Vancouver

Hyde ST, Pedersen MC. Schwarzite nets: a wealth of 3-valent examples sharing similar topologies and symmetries. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2021 Feb 3;477(2246). 20200372. https://doi.org/10.1098/rspa.2020.0372

Author

Hyde, Stephen T. ; Pedersen, Martin Cramer. / Schwarzite nets : a wealth of 3-valent examples sharing similar topologies and symmetries. In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2021 ; Vol. 477, No. 2246.

Bibtex

@article{1681023340b34623bbcb9e8ca9265c13,
title = "Schwarzite nets: a wealth of 3-valent examples sharing similar topologies and symmetries",
abstract = "We enumerate trivalent reticulations of two- and three-periodic hyperbolic surfaces by equal-sided n-gonal faces, (n, 3), where n = 7, 8, 9, 10, 12. These are the simplest hyperbolic generalizations of the planar graphene net, (6, 3) and dodecahedrane, (5, 3). The enumeration proceeds by deleting isometries of regular reticulations of two-dimensional hyperbolic space until the (n, 3) nets can be embedded in euclidean three-space via periodic hyperbolic surfaces. Those nets are then symmetrized in euclidean space retaining their net topology, leading to explicit crystallographic net embeddings whose edges are as equal as possible, affording candidtae patterns for graphitic schwarzites. The resulting schwarzites are the most symmetric examples. More than one hundred topologically distinct nets are described, most of which are novel.",
keywords = "hyperbolic geometry, chemical nets, graph embeddings, symmetry groups, CARBON ALLOTROPES, PATTERNS, SURFACES, KLEIN",
author = "Hyde, {Stephen T.} and Pedersen, {Martin Cramer}",
year = "2021",
month = feb,
day = "3",
doi = "10.1098/rspa.2020.0372",
language = "English",
volume = "477",
journal = "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences",
issn = "1364-5021",
publisher = "The/Royal Society",
number = "2246",

}

RIS

TY - JOUR

T1 - Schwarzite nets

T2 - a wealth of 3-valent examples sharing similar topologies and symmetries

AU - Hyde, Stephen T.

AU - Pedersen, Martin Cramer

PY - 2021/2/3

Y1 - 2021/2/3

N2 - We enumerate trivalent reticulations of two- and three-periodic hyperbolic surfaces by equal-sided n-gonal faces, (n, 3), where n = 7, 8, 9, 10, 12. These are the simplest hyperbolic generalizations of the planar graphene net, (6, 3) and dodecahedrane, (5, 3). The enumeration proceeds by deleting isometries of regular reticulations of two-dimensional hyperbolic space until the (n, 3) nets can be embedded in euclidean three-space via periodic hyperbolic surfaces. Those nets are then symmetrized in euclidean space retaining their net topology, leading to explicit crystallographic net embeddings whose edges are as equal as possible, affording candidtae patterns for graphitic schwarzites. The resulting schwarzites are the most symmetric examples. More than one hundred topologically distinct nets are described, most of which are novel.

AB - We enumerate trivalent reticulations of two- and three-periodic hyperbolic surfaces by equal-sided n-gonal faces, (n, 3), where n = 7, 8, 9, 10, 12. These are the simplest hyperbolic generalizations of the planar graphene net, (6, 3) and dodecahedrane, (5, 3). The enumeration proceeds by deleting isometries of regular reticulations of two-dimensional hyperbolic space until the (n, 3) nets can be embedded in euclidean three-space via periodic hyperbolic surfaces. Those nets are then symmetrized in euclidean space retaining their net topology, leading to explicit crystallographic net embeddings whose edges are as equal as possible, affording candidtae patterns for graphitic schwarzites. The resulting schwarzites are the most symmetric examples. More than one hundred topologically distinct nets are described, most of which are novel.

KW - hyperbolic geometry

KW - chemical nets

KW - graph embeddings

KW - symmetry groups

KW - CARBON ALLOTROPES

KW - PATTERNS

KW - SURFACES

KW - KLEIN

U2 - 10.1098/rspa.2020.0372

DO - 10.1098/rspa.2020.0372

M3 - Journal article

VL - 477

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

IS - 2246

M1 - 20200372

ER -

ID: 276381601