  In this paper, we study the Ehrhart polynomial of the dual of the root
polytope of type C of dimension $d$, denoted by $C_d^*$. We prove that the
roots of the Ehrhart polynomial of $C_d^*$ have the same real part $-1/2$, and
we also prove that the Ehrhart polynomials of $C_d^*$ for $d=1,2,\cdots$ has
the interlacing property.
