Dualities of families of K3 surfaces and strange duality of bimodal singularities

It is introduced by Ebeling and Takahashi that there is a strange duality among invertible polynomials interchanging some invariants of singularities.

In particular, the duality for bimodal singularities are studied by Ebeling and Ploog. 

The aim of my talk is to study dualities of polytope and of lattice for families of K3 surfaces associated to the strange dual pairs of bimodal singularities. 

We conclude that the strange duality can extend to polytope duality, and to lattice duality with some exceptions.