The δ-vectors of reflexive polytopes and of the dual polytopes

Let δ(P) be the δ-vector of a reflexive polytope P⊂Rd of dimension d and δ(P∨) the δ-vector of the dual polytope P∨⊂Rd. In general, δ(P)=δ(P∨) does not hold. In this paper, we give a higher-dimensional construction of a reflexive polytope whose δ-vector equals the δ-vector of the dual polytope. In particular, we consider the case that the reflexive polytope and the dual polytope are unimodularly equivalent.