In this paper we determine the structure of the Chow ring of the Delau
nay-Voronoi compactification (A) over tilde(3) of the moduli space of
principally polarized abelian threefolds. This compactification was in
troduced by Namikawa and studied by Tsushima. We shall use equivariant
classes on level coverings of (A) over tilde(3). We also compare this
ring with the Chow ring of the moduli space of stable genus 3 curves
as determined by Faber.