Finiteness of integral representations on 2-perfect truncation polytopes

Let $P$ be a compact hyperbolic Coxeter truncation polytope of dimension $d\ge 3$, and let $\mathrm{\Gamma }$ be the orbifold fundamental group of the associated Coxeter orbifold ${\mathcal{O}}_P$. Let $\mathcal{G}(\mathrm{\Gamma },G)$ be the geometric component containing the holonomy representation in $\mathrm{Hom}(\mathrm{\Gamma },G)\mathrm{/}G$. $\mathcal{G}(\mathrm{\Gamma },G)$ is identified with the deformation space of properly convex real projective structures on the Coxeter orbifold ${\mathcal{O}}_P$. We prove that $\mathcal{G}(\mathrm{\Gamma },G)$ contains only finitely many integral representations. The same conclusion holds more generally for irreducible, large, $2$-perfect truncation polytopes.