File Name : supp-1_1_2x2.pdf

Caption : trigonal configuration  on a sphere of radius $r = 8\lambda$.}  one $+1$ disclination and  two  $+1/2$ disclinations are located at the vertices of an isosceles triangle inscribed in a great circle (a,b,c). (d) topologically trivial configuration at the south pole. (e--g) the components of the alignment tensor $\vec{n}$ are sketched in (e,f,g).

File Name : supp-1_2x4.pdf

Caption : tetrahedral configuration  on a sphere of radius $r = 10\lambda$.}  the four  $+1/2$ disclinations are located at vertices of tetrahedron (a--d).  the components  of the alignment tensor $\nv$ are sketched in (e--g).

File Name : supp-energies.pdf

Caption : energy contributions for the different equilibrium configurations.} (a) exchange energy. (b) anchoring energy. (c) penalty $w_p$ to satisfy constraints~\eqref{constr}.

File Name : supp-onion.pdf

Caption : onion configuration of the nematic director on the sphere of radius $r = 4\lambda$ ($\lambda =\sqrt{k/(2\varrho)}$.} (a) flux lines of the director field on the sphere. (b--d) components of alignment{tensor} tensor $\nv$.

File Name : supp-squared.pdf

Caption : squared configuration  on a sphere of radius $r = 10\lambda$.}  the four  $+1/2$ disclinations located at the vertices of a square inscribed in a great circle (a--d). the components of the alignment tensor $\nv$ are sketched in  (e--g).