Let W be an irreducible Weyl group and W a its affine Weyl group. In [4] the author defined an affine variety X Wa , called the Shi variety of W a , whose integral points are in bijection with W a . The set of irreducible components of X Wa , denoted H 0 ( X Wa ), is of some interest and we show in this article that H 0 ( X Wa ) has a structure of a semidistributive lattice.