  Let W be a Weyl group, presented as a crystallographic reflection group on a
Euclidean vector space V, and C an open Weyl chamber. In a recent paper,
Waldspurger proved that the images (id-w)(C), for Weyl group elements w, are
all disjoint, and their union is the closed cone spanned by the positive roots.
We show that similarly, if A is the Weyl alcove, the images (id-w)(A), for
affine Weyl group elements w, are all disjoint, and their union is V.
