  We describe a multivariable polynomial invariant for certain class of non
isolated hypersurface singularities generalizing the characteristic polynomial
on monodromy. The starting point is an extension of a theorem due to Le Dung
Trang and K.Saito on commutativity of the local fundamental groups of certain
hypersurfaces. The description of multivariable polynomial invariants is given
in terms of the ideals and polytopes of quasiadjunction generalizing
corresponding data used in the study of the homotopy groups of the complements
to projective hypersurfaces and Alexander invariants of plane reducible curves.
