  We construct global semi-realistic supersymmetric models with intersecting
D6-branes on the non-factorisable orientifold
$T^6/(\mathbb{Z}_4\times\Omega\mathcal{R})$. The non-factorisable structure
gives rise to differences compared to the factorisable case: additional
conditions for the three-cycles to be Lagrangian and extra constraints on the
wrapping numbers for building fractional cycles.
