Spherical nematics with a threefold valence

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.