Riesz basis of exponentials for convex polytopes with symmetric faces

We will discuss a joint result with Nir Lev, which states that for any convex and centrally symmetric polytope $\Omega\subset \mathbb{R}^d$, whose faces of all dimensions are also centrally symmetric, there exists a Riesz basis of exponential functions for $L^2(\Omega)$.
This result extends previously known statements in this direction due to Lyubarskii and Rashkovskii, and also due to Walnut ($d=2$), and by Grepstad and Lev (in arbitrary dimensions), where the same conclusion is obtained under the additional assumption that all the vertices of $\Omega$ lie in the lattice $\mathbb{Z}^d$.