  We perform a complete classification of the flux-induced 12d algebras
compatible with the set of N=1 type II orientifold models that are T-duality
invariant, and allowed by the symmetries of the T^6/(Z_2 x Z_2) isotropic
orbifold. The classification is performed in a type IIB frame, where only H_3
and Q fluxes are present. We then study no-go theorems, formulated in a type
IIA frame, on the existence of Minkowski/de Sitter (Mkw/dS) vacua. By deriving
a dictionary between the sources of potential energy for the three moduli (S, T
and U) in types IIA and IIB, we are able to combine algebra results and no-go
theorems. The outcome is a systematic procedure for identifying
phenomenologically viable models where Mkw/dS vacua may exist. We present a
complete table of the allowed algebras and the viability of their resulting
scalar potential, and we point at the models which stand any chance of
producing a fully stable vacuum.
