  We prove the existence of a family of blow-up solutions of a mean field
equation on sphere. The solutions blow up at four points where the minimum
value of a potential energy function (involving the Green's function) is
attained. The four blow-up points form a regular tetrahedron. Moreover, the
solutions we build have a group of symmetry $T_d$ which is isomorphic to the
symmetric group $S_4$. Other families of solutions can be similarly constructed
with blow-up points at the vertices of equilateral triangles on a great circle
or other inscribed platonic solids (cubes, octahedrons, icosahedrons and
dodecahedrons). All of these solutions have the symmetries of the corresponding
configuration, while they are non-axially symmetric.
