Counting faces of graphical zonotopes

It is a classical fact that the number of vertices of the graphical zonotope $Z_{\mathrm{\Gamma }}$ is equal to the number of acyclic orientations of a graph $\mathrm{\Gamma }$. We show that the $f$-polynomial of $Z_{\mathrm{\Gamma }}$ is obtained as the principal specialization of the $q$-analog of the chromatic symmetric function of $\mathrm{\Gamma }$.