  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.
