Densest plane group packings of regular polygons
Densest plane group packings of regular polygons
Packings of regular convex polygons (n-gons) that are sufficiently dense have been studied extensively in the context of modeling physical and biological systems as well as discrete and computational geometry. Former results were mainly regarding densest lattice or double-lattice configurations. Here we consider all two-dimensional crystallographic symmetry groups (plane groups) by restricting the configuration space of the general packing problem of congruent copies of a compact subset of the two-dimensional Euclidean space to particular isomorphism classes of the discrete group of isometries. We formulate the plane group packing problem as a nonlinear constrained optimization problem. By means of the Entropic Trust Region Packing Algorithm that approximately solves this problem, we examine some known and unknown densest packings of various n-gons in all 17 plane groups and state conjectures about common symmetries of the densest plane group packings for every n-gon.
Torda, Miloslav
184d8a15-4c94-4960-93b0-6c8a9245a681
Goulermas, John Y.
42e3fbd5-39a7-4d25-bc76-4b6361e44fca
Kurlin, Vitaliy
e40698a3-da55-4867-9cbd-3a761528c981
Day, Graeme M.
e3be79ba-ad12-4461-b735-74d5c4355636
7 November 2022
Torda, Miloslav
184d8a15-4c94-4960-93b0-6c8a9245a681
Goulermas, John Y.
42e3fbd5-39a7-4d25-bc76-4b6361e44fca
Kurlin, Vitaliy
e40698a3-da55-4867-9cbd-3a761528c981
Day, Graeme M.
e3be79ba-ad12-4461-b735-74d5c4355636
Torda, Miloslav, Goulermas, John Y., Kurlin, Vitaliy and Day, Graeme M.
(2022)
Densest plane group packings of regular polygons.
Physical Review E, 106 (5), [054603].
(doi:10.1103/PhysRevE.106.054603).
Abstract
Packings of regular convex polygons (n-gons) that are sufficiently dense have been studied extensively in the context of modeling physical and biological systems as well as discrete and computational geometry. Former results were mainly regarding densest lattice or double-lattice configurations. Here we consider all two-dimensional crystallographic symmetry groups (plane groups) by restricting the configuration space of the general packing problem of congruent copies of a compact subset of the two-dimensional Euclidean space to particular isomorphism classes of the discrete group of isometries. We formulate the plane group packing problem as a nonlinear constrained optimization problem. By means of the Entropic Trust Region Packing Algorithm that approximately solves this problem, we examine some known and unknown densest packings of various n-gons in all 17 plane groups and state conjectures about common symmetries of the densest plane group packings for every n-gon.
Text
EV12210
- Accepted Manuscript
Text
EV12210_Supplemental_material
More information
Accepted/In Press date: 18 October 2022
Published date: 7 November 2022
Additional Information:
Funding Information:
The authors thank the Leverhulme Trust for funding this research via the Leverhulme Research Centre for Functional Materials Design.
Publisher Copyright:
© 2022 American Physical Society.
Identifiers
Local EPrints ID: 471580
URI: http://eprints.soton.ac.uk/id/eprint/471580
ISSN: 2470-0045
PURE UUID: 9ce98795-8a85-4372-92ee-178022b3e1eb
Catalogue record
Date deposited: 14 Nov 2022 17:36
Last modified: 17 Mar 2024 03:29
Export record
Altmetrics
Contributors
Author:
Miloslav Torda
Author:
John Y. Goulermas
Author:
Vitaliy Kurlin
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
