Symmetric patterns of dislocations in Thomson's problem

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.