  We use a recent classification of non-degenerate quasihomogeneous polynomials
to construct all Landau-Ginzburg (LG) potentials for N=2 superconformal field
theories with c=9 and calculate the corresponding Hodge numbers. Surprisingly,
the resulting spectra are less symmetric than the existing incomplete results.
It turns out that models belonging to the large class for which an explicit
construction of a mirror model as an orbifold is known show remarkable mirror
symmetry. On the other hand, half of the remaining 15\% of all models have no
mirror partners. This lack of mirror symmetry may point beyond the class of
LG-orbifolds.
