  The moduli space of Frobenius manifolds carries a natural involutive
symmetry, and a distinguished class - so-called modular Frobenius manifolds -
lie at the fixed points of this symmetry. In this paper a classification of
semi-simple modular Frobenius manifolds which are polynomial in all but one of
the variables is begun, and completed for three and four dimensional manifolds.
The resulting examples may also be obtained from higher dimensional manifolds
by a process of folding. The relationship of these results with orbifold
quantum cohomology is also discussed.
