  We perform a systematic search for globally defined MSSM-like and left-right
symmetric models on D6-branes on the T6/Z(2)xZ(6)xOR orientifold with discrete
torsion. Our search is exhaustive for models that are independent of the value
of the one free complex structure modulus. Preliminary investigations suggest
that there exists one prototype of visible sector for MSSM-like and another for
left-right symmetric models with differences arising from various hidden sector
completions to global models. For each prototype, we provide the full matter
spectrum, as well as the Yukawa and other three-point couplings needed to
render vector-like matter states massive. This provides us with tentative
explanations for the mass hierarchies within the quark and lepton sectors. We
also observe that the MSSM-like models correspond to explicit realisations of
the supersymmetric DFSZ axion model, and that the left-right symmetric models
allow for global completions with either completely decoupled hidden sectors or
with some messenger states charged under both visible and hidden gauge groups.
