  We study the Hodge filtration of the intersection cohomology Hodge module for
toric varieties. More precisely, we study the cohomology sheaves of the graded
de Rham complex of the intersection cohomology Hodge module and give a precise
formula relating it with the stalks of the intersection cohomology as a
constructible complex. The main idea is to use the Ishida complex in order to
compute the higher direct images of the sheaf of reflexive differentials.
