  Let (V,W;F) be a weakly reducible, unstabilized, genus three Heegaard
splitting in an orientable, irreducible 3-manifold M and DVW(F) the subset of
the disk complex D(F) consisting of simplices having at least one vertex from V
and at least one vertex from W. In this article, we describe the shape of
DVW(F) and prove that there is a function from the components of DVW(F) to the
isotopy classes of the generalized Heegaard splittings obtained by weak
reductions from (V,W;F), where this function describes how the thick levels are
embedded in the relevant compression bodies.

Geometric Topology