Symmetric patterns of dislocations in Thomson's problem

TL;DR

This paper investigates the symmetric arrangements of dislocations in the classical Thomson's problem, revealing low-energy states with icosahedral symmetry and specific dislocation patterns for certain particle numbers.

Contribution

It introduces a novel application of the ring removal method to identify symmetric dislocation patterns in Thomson's problem.

Findings

Low energy states with icosahedral symmetry identified

Dislocation lines run between 12 disclinations

Method reveals specific symmetric configurations for certain N

Abstract

Determination of the classical ground state arrangement of $N$ charges on the surface of a sphere (Thomson's problem) is a challenging numerical task. For special values of $N$ we have obtained using the ring removal method of Toomre, low energy states in Thomson's problem which have icosahedral symmetry where lines of dislocations run between the 12 disclinations which are induced by the spherical geometry into the near triangular lattice which forms on a local scale.