The topological vertex, introduced by Aganagic-Klemm-Marino-Vafa, is a combinatorial gadget for calculating Donaldson-Thomas invariants of toric Calabi-Yau threefolds. Yet, in Jim's banana talk last week, we saw him use it for a *non-toric* Calabi-Yau threefold. In this talk I explain in some more detail how and why the topological vertex can indeed be used in some non-toric settings. I illustrate this in the (simpler) case of local elliptic surfaces, which leads to a new way of finding the Katz-Klemm-Vafa formula.