  We evaluate the three-photon vertex functions at order $B$ and $B^{2}$ in a
weak constant magnetic field at finite temperature and density with on shell
external lines. Their application to the study of the photon splitting process
leads to consider high energy photons whose dispersion relations are not
changed significantly by the plasma effects. The absorption coefficient is
computed and compared with the perturbative vacuum result. For the values of
temperature and density of some astrophysical objects with a weak magnetic
field, the matter effects are negligible.
