  A. Girand has constructed an explicit two-parameter family of flat
connections over the complex projective plane $\mathbb{P}^2$. These connections
have dihedral monodromy and their polar locus is a prescribed quintic composed
of a conic and three tangent lines. In this paper, we give a generalization of
this construction. That is, we construct an explicit $n$-parameter family of
flat connections over the complex projective space $\mathbb{P}^n$. Moreover, we
discuss the relation between these connections and the Garnier system.
