  We present a theoretical study of the energetics of thin nematic shells with
two charge one-half defects and one charge-one defect. We determine the optimal
arrangement: the defects are located on a great circle at the vertices of an
isosceles triangle with angles of 66 degrees at the charge one-half defects and
a distinct angle of 48 degrees, consistent with experimental findings. We also
analyse thermal fluctuations around this ground state and estimate the energy
as a function of thickness. We find that the energy of the three-defect shell
is close to the energy of other known configurations having two charge-one and
four charge one-half defects. This finding, together with the large energy
barriers separating one configuration from the others, explains their
observation in experiments as well as their long-time stability.
