  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.
