# degenerate abelian surfaces

I am wondering if the family of degenerate abelian surfaces constructed by K. Hulek, C. Kahn and S.H. Weintraub in "Moduli spaces of Abelian Surfaces: Compactification, Degenarations, and Theta Functions" is a toroidal degeneration, i.e. if we let $\mathcal{X}_2 \to \mathcal{A}_2$ be the universal family of principally polarized abelian surfaces and $\tilde{\mathcal{X}} \to \tilde{\mathcal{A}}$ its degenerate famiy (here $\tilde{\mathcal{A}}$ stands for the Igusa compactification) then is it true that $(\mathcal{X}, \mathcal{A})$ is a toroidal compactification?