Abstract
It is shown that reduction of the symmetry of the shape of almost spherical nanocrystals to that of a three axial ellipsoid or lower leads to a splitting of the exciton radiative doublets into linearly polarized components. The splitting is a result of a combined action of the distortion of the boundary conditions and the electron-hole exchange interaction. Both the short-range and the long-range parts of the exchange interaction are equally important for the splitting.