  We discuss how the experimental neutrino oscillation data can be realized in
the framework of the baryon triality ($B_3$) constrained supersymmetric
Standard Model (cSSM). We show how to obtain phenomenologically viable
solutions, which are compatible with the recent WMAP observations. We present
results for the hierarchical, inverted and degenerate cases which illustrate
the possible size and structure of the lepton number violating couplings. We
work with a new, as yet unpublished version of SOFTSUSY, where we implemented
full one--loop neutrino masses. Finally, we shortly discuss some
phenomenological implications at the LHC.
