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As a discrete analog to Minkowski's theorem on convex bodies, Willsconjectured that the Ehrhart coefficients of a centrally symmetric latticepolytope with exactly one interior lattice point are maximized by those of thecube of side length two. We discuss several counterexamples to this conjectureand, on the positive side, we identify a family of lattice polytopes thatfulfill the claimed inequalities. This family is related to the recentlyintroduced class of $l$-reflexive polytopes.

On counterexamples to a conjecture of Wills and Ehrhart polynomials whose roots have equal real parts