Duality of Weights, Mirror Symmetry and Arnold's Strange Duality

A notion of duality of weight systems which corresponds to Batyrev's toric mirror symmetry is given. Explicit duality on the (1,1)-cohomology of K3 surfaces which are minimal models of toric hypersurfaces is constructed using monomial divisor mirror map of Aspinwall-Greene-Morrison. It is shown that Arnold's strange duality for exceptional unimodal singularities reduces to this duality.