Orientifold's Landscape: Non-Factorisable Six-Tori

We construct type IIA orientifolds on T6/(Z2 x Z2) which admit non factorisable lattices. We describe a method to deal with this kind of configurations and discuss how the compactification lattice affects the tadpole cancellation conditions. Moreover, we include D6-branes which are not parallel to O6-planes. These branes can give rise to chiral spectra in four dimensions, thus uncovering a new corner in the landscape of intersecting D-brane model constructions. We demonstrate the construction at an explicit example. In general we argue that obtaining an odd number of families is problematic.