  The orbits space of an irreducible representation of a finite group is a
variety whose coordinate ring is finitely generated by homogeneous invariant
polynomials. Boris Dubrovin showed that the orbits spaces of the reflection
groups acquire the structure of polynomial Frobenius manifolds. Dubrovin's
method to construct examples of Frobenius manifolds on orbits spaces was
carried for other linear representations of discrete groups which have in
common that the coordinate rings of the the orbits spaces are polynomial rings.
In this article, we show that the orbits space of an irreducible representation
of a Dicyclic group acquire two structures of Frobenius manifolds. The
coordinate ring of this orbits space is not a polynomial ring.
