Periodic entanglement III: Tangled degree-3 finite and layer net intergrowths from rare forests

Myfanwy E. Evans; Stephen T. Hyde

doi:10.1107/S2053273315014710

Periodic entanglement III: Tangled degree-3 finite and layer net intergrowths from rare forests

Myfanwy E. Evans^*, Stephen T. Hyde

^*Corresponding author for this work

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

6 Citations (Scopus)

Abstract

Entanglements of two-dimensional honeycomb nets are constructed from free tilings of the hyperbolic plane (H²) on triply periodic minimal surfaces. The 2-periodic nets that comprise the structures are guaranteed by considering regular, rare free tilings in H². This paper catalogues an array of entanglements that are both beautiful and challenging for current classification techniques, including examples that are realized in metal-organic materials. The compactification of these structures to the genus-3 torus is considered as a preliminary method for generating entanglements of finite θ-graphs, potentially useful for gaining insight into the entanglement of the periodic structure. This work builds on previous structural enumerations given in Periodic entanglement Parts I and II [Evans et al. (2013). Acta Cryst. A69, 241-261; Evans et al. (2013). Acta Cryst. A69, 262-275].

Original language	English
Pages (from-to)	599-611
Number of pages	13
Journal	Acta Crystallographica Section A: Foundations and Advances
Volume	71
DOIs	https://doi.org/10.1107/S2053273315014710
Publication status	Published - 2015

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title = "Periodic entanglement III: Tangled degree-3 finite and layer net intergrowths from rare forests",

abstract = "Entanglements of two-dimensional honeycomb nets are constructed from free tilings of the hyperbolic plane (H2) on triply periodic minimal surfaces. The 2-periodic nets that comprise the structures are guaranteed by considering regular, rare free tilings in H2. This paper catalogues an array of entanglements that are both beautiful and challenging for current classification techniques, including examples that are realized in metal-organic materials. The compactification of these structures to the genus-3 torus is considered as a preliminary method for generating entanglements of finite θ-graphs, potentially useful for gaining insight into the entanglement of the periodic structure. This work builds on previous structural enumerations given in Periodic entanglement Parts I and II [Evans et al. (2013). Acta Cryst. A69, 241-261; Evans et al. (2013). Acta Cryst. A69, 262-275].",

keywords = "Borromean nets, catenation, crystal nets, enumeration, frameworks, graphs, hyperbolic reticulations, networks, periodic entanglement, surfaces, tilings",

author = "Evans, {Myfanwy E.} and Hyde, {Stephen T.}",

note = "Publisher Copyright: {\textcopyright} 2015 International Union of Crystallography.",

year = "2015",

doi = "10.1107/S2053273315014710",

language = "English",

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journal = "Acta Crystallographica Section A: Foundations and Advances",

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publisher = "John Wiley & Sons Inc.",

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TY - JOUR

T1 - Periodic entanglement III

T2 - Tangled degree-3 finite and layer net intergrowths from rare forests

AU - Evans, Myfanwy E.

AU - Hyde, Stephen T.

PY - 2015

Y1 - 2015

N2 - Entanglements of two-dimensional honeycomb nets are constructed from free tilings of the hyperbolic plane (H2) on triply periodic minimal surfaces. The 2-periodic nets that comprise the structures are guaranteed by considering regular, rare free tilings in H2. This paper catalogues an array of entanglements that are both beautiful and challenging for current classification techniques, including examples that are realized in metal-organic materials. The compactification of these structures to the genus-3 torus is considered as a preliminary method for generating entanglements of finite θ-graphs, potentially useful for gaining insight into the entanglement of the periodic structure. This work builds on previous structural enumerations given in Periodic entanglement Parts I and II [Evans et al. (2013). Acta Cryst. A69, 241-261; Evans et al. (2013). Acta Cryst. A69, 262-275].

AB - Entanglements of two-dimensional honeycomb nets are constructed from free tilings of the hyperbolic plane (H2) on triply periodic minimal surfaces. The 2-periodic nets that comprise the structures are guaranteed by considering regular, rare free tilings in H2. This paper catalogues an array of entanglements that are both beautiful and challenging for current classification techniques, including examples that are realized in metal-organic materials. The compactification of these structures to the genus-3 torus is considered as a preliminary method for generating entanglements of finite θ-graphs, potentially useful for gaining insight into the entanglement of the periodic structure. This work builds on previous structural enumerations given in Periodic entanglement Parts I and II [Evans et al. (2013). Acta Cryst. A69, 241-261; Evans et al. (2013). Acta Cryst. A69, 262-275].

KW - Borromean nets

KW - catenation

KW - crystal nets

KW - enumeration

KW - frameworks

KW - graphs

KW - hyperbolic reticulations

KW - networks

KW - periodic entanglement

KW - surfaces

KW - tilings

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DO - 10.1107/S2053273315014710

M3 - Article

SN - 0108-7673

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EP - 611

JO - Acta Crystallographica Section A: Foundations and Advances

JF - Acta Crystallographica Section A: Foundations and Advances

ER -

Periodic entanglement III: Tangled degree-3 finite and layer net intergrowths from rare forests

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