Centrally symmetric configurations of order polytopes

It is shown that the toric ideal of the centrally symmetric configuration of the order polytope of a finite partially ordered set possesses a squarefree quadratic initial ideal. It then follows that the convex polytope arising from the centrally symmetric configuration of an order polytope is a normal Gorenstein Fano polytope.Comment: 9 pages, Proof of Theorem 2.2 is simplified. Major revision on Section