  Given the toric (or toral) arrangement defined by a root system $\Phi$, we
describe the poset of its layers (connected components of intersections) and we
count its elements. Indeed we show how to reduce to zero-dimensional layers,
and in this case we provide an explicit formula involving the maximal
subdiagrams of the affine Dynkin diagram of $\Phi$. Then we compute the Euler
characteristic and the Poincare' polynomial of the complement of the
arrangement, which is the set of regular points of the torus.
