Towards enumeration of crystalline frameworks: the 2D hyperbolic approach

S. T. Hyde; O. Delgado Friedrichs; S. J. Ramsden; V. Robins

doi:10.1016/j.solidstatesciences.2006.04.001

Towards enumeration of crystalline frameworks: the 2D hyperbolic approach

S. T. Hyde^*, O. Delgado Friedrichs, S. J. Ramsden, V. Robins

^*Corresponding author for this work

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

80 Citations (Scopus)

Abstract

Crystalline frameworks in 3D Euclidean space can be constructed by projecting tilings of 2D hyperbolic space onto three-periodic minimal surfaces, giving surface reticulations. The technique involves Delaney-Dress tiling theory, group theory, differential and non-Euclidean geometry. Preliminary results of this approach, found at http://epinet.anu.edu.au, are discussed and compared with other approaches. Crown

Original language	English
Pages (from-to)	740-752
Number of pages	13
Journal	Solid State Sciences
Volume	8
Issue number	7
DOIs	https://doi.org/10.1016/j.solidstatesciences.2006.04.001
Publication status	Published - Jul 2006

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title = "Towards enumeration of crystalline frameworks: the 2D hyperbolic approach",

abstract = "Crystalline frameworks in 3D Euclidean space can be constructed by projecting tilings of 2D hyperbolic space onto three-periodic minimal surfaces, giving surface reticulations. The technique involves Delaney-Dress tiling theory, group theory, differential and non-Euclidean geometry. Preliminary results of this approach, found at http://epinet.anu.edu.au, are discussed and compared with other approaches. Crown",

keywords = "Frameworks, Hyperbolic tilings, Minimal surfaces, Networks, Reticular chemistry, Symmetry groups",

author = "Hyde, {S. T.} and {Delgado Friedrichs}, O. and Ramsden, {S. J.} and V. Robins",

year = "2006",

month = jul,

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journal = "Solid State Sciences",

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T2 - the 2D hyperbolic approach

AU - Hyde, S. T.

AU - Delgado Friedrichs, O.

AU - Ramsden, S. J.

AU - Robins, V.

PY - 2006/7

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AB - Crystalline frameworks in 3D Euclidean space can be constructed by projecting tilings of 2D hyperbolic space onto three-periodic minimal surfaces, giving surface reticulations. The technique involves Delaney-Dress tiling theory, group theory, differential and non-Euclidean geometry. Preliminary results of this approach, found at http://epinet.anu.edu.au, are discussed and compared with other approaches. Crown

KW - Frameworks

KW - Hyperbolic tilings

KW - Minimal surfaces

KW - Networks

KW - Reticular chemistry

KW - Symmetry groups

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U2 - 10.1016/j.solidstatesciences.2006.04.001

DO - 10.1016/j.solidstatesciences.2006.04.001

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VL - 8

SP - 740

EP - 752

JO - Solid State Sciences

JF - Solid State Sciences

IS - 7

ER -

Towards enumeration of crystalline frameworks: the 2D hyperbolic approach

Abstract

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