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 that have icosahedral symmetry. Lines of dislocations run between the 12 disclinations which are induced by the spherical geometry into the near triangular lattice that forms on a local scale.

• Received 17 May 1999

DOI:https://doi.org/10.1103/PhysRevB.60.15628