Symmetry groups and reticulations of the hexagonal H surface

Vanessa Robins; S. J. Ramsden; Stephen T. Hyde

doi:10.1016/j.physa.2004.03.053

Symmetry groups and reticulations of the hexagonal H surface

Vanessa Robins^*, S. J. Ramsden, Stephen T. Hyde

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

12 Citations (Scopus)

Abstract

We describe a systematic approach to generate nets that arise from decorations of periodic minimal surfaces. Such surfaces are covered by the hyperbolic plane, in the same way that the euclidean plane covers a cylinder. Thus, a symmetric hyperbolic network can be wrapped onto an appropriate minimal surface to obtain a 3D periodic net. This requires symmetries of the hyperbolic net to match the symmetries of the minimal surface. Here, we tabulate all such symmetry groups that are compatible with the H minimal surface.

Original language	English
Pages (from-to)	173-180
Number of pages	8
Journal	Physica A: Statistical Mechanics and its Applications
Volume	339
Issue number	1-2
DOIs	https://doi.org/10.1016/j.physa.2004.03.053
Publication status	Published - 1 Aug 2004
Event	Proceedings of the International Conference New Materials - Canberra, Vic., Australia Duration: 3 Nov 2003 → 7 Nov 2003

Access to Document

10.1016/j.physa.2004.03.053

Cite this

@article{eaac8efa77dd4e089e9e841a6b9a62ae,

title = "Symmetry groups and reticulations of the hexagonal H surface",

abstract = "We describe a systematic approach to generate nets that arise from decorations of periodic minimal surfaces. Such surfaces are covered by the hyperbolic plane, in the same way that the euclidean plane covers a cylinder. Thus, a symmetric hyperbolic network can be wrapped onto an appropriate minimal surface to obtain a 3D periodic net. This requires symmetries of the hyperbolic net to match the symmetries of the minimal surface. Here, we tabulate all such symmetry groups that are compatible with the H minimal surface.",

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

author = "Vanessa Robins and Ramsden, {S. J.} and Hyde, {Stephen T.}",

year = "2004",

month = aug,

day = "1",

doi = "10.1016/j.physa.2004.03.053",

language = "English",

volume = "339",

pages = "173--180",

journal = "Physica A: Statistical Mechanics and its Applications",

issn = "0378-4371",

publisher = "Elsevier B.V.",

number = "1-2",

note = "Proceedings of the International Conference New Materials ; Conference date: 03-11-2003 Through 07-11-2003",

}

TY - JOUR

T1 - Symmetry groups and reticulations of the hexagonal H surface

AU - Robins, Vanessa

AU - Ramsden, S. J.

AU - Hyde, Stephen T.

PY - 2004/8/1

Y1 - 2004/8/1

N2 - We describe a systematic approach to generate nets that arise from decorations of periodic minimal surfaces. Such surfaces are covered by the hyperbolic plane, in the same way that the euclidean plane covers a cylinder. Thus, a symmetric hyperbolic network can be wrapped onto an appropriate minimal surface to obtain a 3D periodic net. This requires symmetries of the hyperbolic net to match the symmetries of the minimal surface. Here, we tabulate all such symmetry groups that are compatible with the H minimal surface.

AB - We describe a systematic approach to generate nets that arise from decorations of periodic minimal surfaces. Such surfaces are covered by the hyperbolic plane, in the same way that the euclidean plane covers a cylinder. Thus, a symmetric hyperbolic network can be wrapped onto an appropriate minimal surface to obtain a 3D periodic net. This requires symmetries of the hyperbolic net to match the symmetries of the minimal surface. Here, we tabulate all such symmetry groups that are compatible with the H minimal surface.

KW - Frameworks

KW - Hyperbolic tilings

KW - Minimal surfaces

KW - Networks

KW - Reticular chemistry

KW - Symmetry groups

UR - http://www.scopus.com/inward/record.url?scp=2942609450&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2004.03.053

DO - 10.1016/j.physa.2004.03.053

M3 - Conference article

SN - 0378-4371

VL - 339

SP - 173

EP - 180

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 1-2

T2 - Proceedings of the International Conference New Materials

Y2 - 3 November 2003 through 7 November 2003

ER -

Symmetry groups and reticulations of the hexagonal H surface

Abstract

Access to Document

Other files and links

Fingerprint

Cite this