  A lattice polytope $\mathcal{P} \subset \mathbb{R}^d$ is called a locally
anti-blocking polytope if for any closed orthant $\mathbb{R}^d_{\varepsilon}$
in $\mathbb{R}^d$, $\mathcal{P} \cap \mathbb{R}^d_{\varepsilon}$ is
unimodularly equivalent to an anti-blocking polytope by reflections of
coordinate hyperplanes. In the present paper, we give a formula for the
$h^*$-polynomials of locally anti-blocking lattice polytopes. In particular, we
discuss the $\gamma$-positivity of the $h^*$-polynomials of locally
anti-blocking reflexive polytopes.
