Densest plane group packings of regular polygons

Torda, Miloslav, Goulermas, John Y, Kurlin, Vitaliy ORCID: 0000-0001-5328-5351 and Day, Graeme M (2022) Densest plane group packings of regular polygons. PHYSICAL REVIEW E, 106 (5). 054603-.

Access the full-text of this item by clicking on the Open Access link.

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.

Item Type:	Article
Depositing User:	Symplectic Admin
Date Deposited:	02 Dec 2022 09:02
Last Modified:	25 Jan 2023 10:01
DOI:	10.1103/PhysRevE.106.054603
Open Access URL:	https://arxiv.org/abs/2207.08959
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3166465