  We show that combined permanent and induced electric dipole interactions of
polar and polarizable molecules with collinear electric fields lead to a sui
generis topology of the corresponding Stark energy surfaces and of other
observables - such as alignment and orientation cosines - in the plane spanned
by the permanent and induced dipole interaction parameters. We find that the
loci of the intersections of the surfaces can be traced analytically and that
the eigenstates as well as the number of their intersections can be
characterized by a single integer index. The value of the index, distinctive
for a particular ratio of the interaction parameters, brings out a close
kinship with the eigenproperties obtained previously for a class of Stark
states via the apparatus of supersymmetric quantum mechanics.
