Spheres in laser material studies or useful simplifications brought by 'ascending' symmetries

It is shown that looking for quasi-spheres allows one to describe the complex spectra of an Er3+-doped silicate glass near 1500 nm in a simple way. It is shown that 'ascending' the symmetry from the generally accepted point symmetry C-2v to the pure icosahedral symmetry, brings practical simplification. Looking for a spherical approximation in the crystal field parameter space, brings further simplification through use of the N-v scalar crystal field parameter describing the maximum crystal field splitting of a given J-state. The B-0(6), B-3(6) and B-6(6) icosahedral crystal field values are deduced from it. Such effective ascending symmetry may be of practical importance knowing that the considered I-4(13/2) <----> I-4(15/2) transition of Er3+ in silica glasses rules the universally adopted optical amplification in glass fibre telecommunication networks.