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

Let delta(P) be the delta-vector of a reflexive polytope P subset of R-d of dimension d and delta(P-v) the delta-vector of the dual polytope p(v) subset of R-d. In general, delta(P) = delta(P-v) does not hold. In this paper, we give a higher-dimensional construction of a reflexive polytope whose delta-vector equals the delta-vector of the dual polytope. In particular, we consider the case that the reflexive polytope and the dual polytope are unimodularly equivalent (C) 2016 Elsevier B.V. All rights reserved.