  We provide an explicit bijection between the ad-nilpotent ideals of a Borel
subalgebra of a simple Lie algebra g and the orbits of \check{Q}/(h+1)\check{Q}
under the Weyl group (\check{Q} being the coroot lattice and h the Coxeter
number of g). From this result we deduce in a uniform way a counting formula
for the ad-nilpotent ideals.
