We use the decomposition theorem for the blowdown map from a toroidal compactification of the moduli space of abelian varieties to its Satake compactification to compute the intersection cohomology for these compactifications in low genus. Intersection homology is a homology theory for singular spaces that has Poincare duality, and decomposition theorem relates it for the source and target of a morphism, and we will focus on reviewing how this machinery works in general, and in our case. Based on joint work with Klaus Hulek.