  Let $W$ be a irreducible Weyl group and $W_a$ its affine Weyl group. In a
previous article the author defined an affine variety $\widehat{X}_{W_a}$,
called the Shi variety of $W_a$, whose integral points are in bijection with
$W_a$. The set of irreducible components of $\widehat{X}_{W_a}$, denoted
$H^0(\widehat{X}_{W_a})$, is of some interest and we show in this article that
$H^0(\widehat{X}_{W_a})$ has a structure of semidistributive lattice.
