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Isotopy classes for 3-periodic net embeddings

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Isotopy classes for 3-periodic net embeddings. / Power, Stephen; Baburin, Igor; Proserpio, Davide.
In: Acta Crystallographica Section A: Foundations and Advances, Vol. 76, No. 3, 01.05.2020, p. 275-301.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Power, S, Baburin, I & Proserpio, D 2020, 'Isotopy classes for 3-periodic net embeddings', Acta Crystallographica Section A: Foundations and Advances, vol. 76, no. 3, pp. 275-301. https://doi.org/10.1107/S2053273320000625

APA

Power, S., Baburin, I., & Proserpio, D. (2020). Isotopy classes for 3-periodic net embeddings. Acta Crystallographica Section A: Foundations and Advances, 76(3), 275-301. https://doi.org/10.1107/S2053273320000625

Vancouver

Power S, Baburin I, Proserpio D. Isotopy classes for 3-periodic net embeddings. Acta Crystallographica Section A: Foundations and Advances. 2020 May 1;76(3):275-301. Epub 2020 Mar 5. doi: 10.1107/S2053273320000625

Author

Power, Stephen ; Baburin, Igor ; Proserpio, Davide. / Isotopy classes for 3-periodic net embeddings. In: Acta Crystallographica Section A: Foundations and Advances. 2020 ; Vol. 76, No. 3. pp. 275-301.

Bibtex

@article{154e66faf2d146188d38a433d11671f7,
title = "Isotopy classes for 3-periodic net embeddings",
abstract = "Entangled embedded periodic nets and crystal frameworks are defined, along with their {dimension type}, {homogeneity type}, {adjacency depth} and {periodic isotopy type}. We obtain periodic isotopy classifications for various families of embedded nets with small quotient graphs. We enumerate the 25 periodic isotopy classes of depth 1 embedded nets with a single vertex quotient graph. Additionally, we classify embeddings of n-fold copies of {pcu} with all connected components in a parallel orientation and n vertices in a repeat unit, and determine their maximal symmetry periodic isotopes. We also introduce the methodology of linear graph knots on the flat 3-torus [0, 1)^3. These graph knots, with linear edges, are spatial embeddings of the labelled quotient graphs of an embedded net which are associated with its periodicity bases.",
keywords = "periodic nets, embedded nets, coordination polymers, isotopy types, crystallographic frameworks",
author = "Stephen Power and Igor Baburin and Davide Proserpio",
note = "{\textcopyright} International Union of Crystallography",
year = "2020",
month = may,
day = "1",
doi = "10.1107/S2053273320000625",
language = "English",
volume = "76",
pages = "275--301",
journal = "Acta Crystallographica Section A: Foundations and Advances",
issn = "2053-2733",
publisher = "Wiley",
number = "3",

}

RIS

TY - JOUR

T1 - Isotopy classes for 3-periodic net embeddings

AU - Power, Stephen

AU - Baburin, Igor

AU - Proserpio, Davide

N1 - © International Union of Crystallography

PY - 2020/5/1

Y1 - 2020/5/1

N2 - Entangled embedded periodic nets and crystal frameworks are defined, along with their {dimension type}, {homogeneity type}, {adjacency depth} and {periodic isotopy type}. We obtain periodic isotopy classifications for various families of embedded nets with small quotient graphs. We enumerate the 25 periodic isotopy classes of depth 1 embedded nets with a single vertex quotient graph. Additionally, we classify embeddings of n-fold copies of {pcu} with all connected components in a parallel orientation and n vertices in a repeat unit, and determine their maximal symmetry periodic isotopes. We also introduce the methodology of linear graph knots on the flat 3-torus [0, 1)^3. These graph knots, with linear edges, are spatial embeddings of the labelled quotient graphs of an embedded net which are associated with its periodicity bases.

AB - Entangled embedded periodic nets and crystal frameworks are defined, along with their {dimension type}, {homogeneity type}, {adjacency depth} and {periodic isotopy type}. We obtain periodic isotopy classifications for various families of embedded nets with small quotient graphs. We enumerate the 25 periodic isotopy classes of depth 1 embedded nets with a single vertex quotient graph. Additionally, we classify embeddings of n-fold copies of {pcu} with all connected components in a parallel orientation and n vertices in a repeat unit, and determine their maximal symmetry periodic isotopes. We also introduce the methodology of linear graph knots on the flat 3-torus [0, 1)^3. These graph knots, with linear edges, are spatial embeddings of the labelled quotient graphs of an embedded net which are associated with its periodicity bases.

KW - periodic nets

KW - embedded nets

KW - coordination polymers

KW - isotopy types

KW - crystallographic frameworks

U2 - 10.1107/S2053273320000625

DO - 10.1107/S2053273320000625

M3 - Journal article

VL - 76

SP - 275

EP - 301

JO - Acta Crystallographica Section A: Foundations and Advances

JF - Acta Crystallographica Section A: Foundations and Advances

SN - 2053-2733

IS - 3

ER -