Hyperbolic crystallography of two-periodic surfaces and associated structures

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Hyperbolic crystallography of two-periodic surfaces and associated structures. / Pedersen, Martin Cramer; Hyde, Stephen T.

In: Acta Crystallographica Section A: Foundations and Advances, Vol. 73, No. 2, 01.03.2017, p. 124-134.

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

Harvard

Pedersen, MC & Hyde, ST 2017, 'Hyperbolic crystallography of two-periodic surfaces and associated structures', Acta Crystallographica Section A: Foundations and Advances, vol. 73, no. 2, pp. 124-134. https://doi.org/10.1107/S2053273316019112

APA

Pedersen, M. C., & Hyde, S. T. (2017). Hyperbolic crystallography of two-periodic surfaces and associated structures. Acta Crystallographica Section A: Foundations and Advances, 73(2), 124-134. https://doi.org/10.1107/S2053273316019112

Vancouver

Pedersen MC, Hyde ST. Hyperbolic crystallography of two-periodic surfaces and associated structures. Acta Crystallographica Section A: Foundations and Advances. 2017 Mar 1;73(2):124-134. https://doi.org/10.1107/S2053273316019112

Author

Pedersen, Martin Cramer ; Hyde, Stephen T. / Hyperbolic crystallography of two-periodic surfaces and associated structures. In: Acta Crystallographica Section A: Foundations and Advances. 2017 ; Vol. 73, No. 2. pp. 124-134.

Bibtex

@article{3b700a6eff0642248d669af0c47e2575,
title = "Hyperbolic crystallography of two-periodic surfaces and associated structures",
abstract = "This paper describes the families of the simplest, two-periodic constant mean curvature surfaces, the genus-two HCB and SQL surfaces, and their isometries. All the discrete groups that contain the translations of the genus-two surfaces embedded in Euclidean three-space modulo the translation lattice are derived and enumerated. Using this information, the subgroup lattice graphs are constructed, which contain all of the group-subgroup relations of the aforementioned quotient groups. The resulting groups represent the two-dimensional representations of subperiodic layer groups with square and hexagonal supergroups, allowing exhaustive enumeration of tilings and associated patterns on these surfaces. Two examples are given: a two-periodic [3,7]-tiling with hyperbolic orbifold symbol and a surface decoration.The intrinsic, hyperbolic crystallography of the two-periodic, genus-two HCB and SQL surfaces is presented. All discrete groups containing the translations of the Euclidean embeddings of these surfaces are derived and examples of applications are given.",
keywords = "constant mean curvature surfaces, hyperbolic crystallography, hyperbolic geometry",
author = "Pedersen, {Martin Cramer} and Hyde, {Stephen T.}",
year = "2017",
month = mar,
day = "1",
doi = "10.1107/S2053273316019112",
language = "English",
volume = "73",
pages = "124--134",
journal = "Acta Crystallographica Section A: Foundations and Advances",
issn = "0108-7673",
publisher = "Wiley",
number = "2",

}

RIS

TY - JOUR

T1 - Hyperbolic crystallography of two-periodic surfaces and associated structures

AU - Pedersen, Martin Cramer

AU - Hyde, Stephen T.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - This paper describes the families of the simplest, two-periodic constant mean curvature surfaces, the genus-two HCB and SQL surfaces, and their isometries. All the discrete groups that contain the translations of the genus-two surfaces embedded in Euclidean three-space modulo the translation lattice are derived and enumerated. Using this information, the subgroup lattice graphs are constructed, which contain all of the group-subgroup relations of the aforementioned quotient groups. The resulting groups represent the two-dimensional representations of subperiodic layer groups with square and hexagonal supergroups, allowing exhaustive enumeration of tilings and associated patterns on these surfaces. Two examples are given: a two-periodic [3,7]-tiling with hyperbolic orbifold symbol and a surface decoration.The intrinsic, hyperbolic crystallography of the two-periodic, genus-two HCB and SQL surfaces is presented. All discrete groups containing the translations of the Euclidean embeddings of these surfaces are derived and examples of applications are given.

AB - This paper describes the families of the simplest, two-periodic constant mean curvature surfaces, the genus-two HCB and SQL surfaces, and their isometries. All the discrete groups that contain the translations of the genus-two surfaces embedded in Euclidean three-space modulo the translation lattice are derived and enumerated. Using this information, the subgroup lattice graphs are constructed, which contain all of the group-subgroup relations of the aforementioned quotient groups. The resulting groups represent the two-dimensional representations of subperiodic layer groups with square and hexagonal supergroups, allowing exhaustive enumeration of tilings and associated patterns on these surfaces. Two examples are given: a two-periodic [3,7]-tiling with hyperbolic orbifold symbol and a surface decoration.The intrinsic, hyperbolic crystallography of the two-periodic, genus-two HCB and SQL surfaces is presented. All discrete groups containing the translations of the Euclidean embeddings of these surfaces are derived and examples of applications are given.

KW - constant mean curvature surfaces

KW - hyperbolic crystallography

KW - hyperbolic geometry

UR - http://www.scopus.com/inward/record.url?scp=85014351462&partnerID=8YFLogxK

U2 - 10.1107/S2053273316019112

DO - 10.1107/S2053273316019112

M3 - Journal article

AN - SCOPUS:85014351462

VL - 73

SP - 124

EP - 134

JO - Acta Crystallographica Section A: Foundations and Advances

JF - Acta Crystallographica Section A: Foundations and Advances

SN - 0108-7673

IS - 2

ER -

ID: 229370446