Nill's facet bound conjecture for reflexive polytopes

Let ${\mathcal P}$ be a $d$-dimensional reflexive polytope, meaning a lattice polytope whose polar dual is also a lattice polytope after placing the origin in its interior. Let $N({\mathcal P})$ denote the number of facets of ${\mathcal P}$. Nill's conjecture.

$$N({\mathcal P}) \leq 6^{d/2}.$$

This is a facet bound for reflexive polytopes and is presented as a conjecture of Nill. The paper notes that symmetric edge polytopes are centrally symmetric reflexive polytopes, so its results for these polytopes provide a partial answer; the general assertion remains unresolved in the supplied context.