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Markushevich and Tikhomirov provided a construction of an irreduciblesymplectic V-manifold of dimension 4, the relative compactified Prym variety ofa family of curves with involution, which is a Lagrangian fibration withpolarization of type (1,2). We give a characterization of the dual Lagrangianfibration. We also identify the moduli space of Lagrangian fibrations of thistype and show that the duality defines a rational involution on it.

Duality for relative Prymians associated to K3 double covers of del Pezzo surface of degree 2