Hurwitz spaces are spaces of pairs (S, f) where S is a Riemann surface and f : S → ℂ̂ a meromorphicfunction. In this work, we study 1-dimensional Hurwitz spaces HDp of meromorphic p-fold functions with four branched points, three of them fixed; the corresponding monodromy representation over each branched point is a product of (p - 1)/2 transpositions and the monodromy groupis the dihedral group Dp. We prove that the completion HDp of the Hurwitz space HDp is uniformized by a non-nomal index p + 1 subgroup of a triangular group with signature (0; [p, p, p]). We also establish the relation of the meromorphic covers with elliptic functions and show that HDp is aquotient of the upper half plane by the modular group Γ (2) ∩ Γ0 (p). Finally, we study the real forms of the Belyi projection HDp → ℂ̂ and show that there are two nonbicoformal equivalent such real forms which are topologically conjugated.