  The interior polynomial is an invariant of (signed) bipartite graphs, and the
interior polynomial of a plane bipartite graph is equal to a part of the HOMFLY
polynomial of a naturally associated link. The HOMFLY polynomial $P_L(v,z)$ is
a famous link invariant with many known properties. For example, the HOMFLY
polynomial of the mirror image of $L$ is given by $P_{L}(-v^{-1},z)$. This
implies a property of the interior polynomial in the planar case. We prove that
the same property holds for any bipartite graph. The proof relies on Ehrhart
reciprocity applied to the so called root polytope. We also establish formulas
for the interior polynomial inspired by the knot theoretical notions of flyping
and mutation.
