Suppose after normalising by powers of $t$, the dominant monomials are $(z_{1}z_{2})^{-1},-(z_{1}z_{2})^{-1}z_{3},-1$, so the hypersurface admits the local complex geometric model $\{(z_{1}z_{2})^{-1}(1-z_{3})=1\}\subset(\mathbb{C}^{*})^{4}_{z_{0},z_{1},z_{2},z_{3}}$, or equivalently $z_{1}z_{2}=1-z_{3}$. This happens near the intersection of two smooth components of the toric boundary. Up to numerical factors, the holomorphic volume form is given by

$$\frac{dz_{0}}{z_{0}}\wedge\frac{dz_{1}}{z_{1}}\wedge\frac{dz_{2}}{z_{2}}\wedge\frac{dz_{3}}{z_{3}}=d((z_{1}z_{2})^{-1}(1-z_{3})-1)\wedge\Omega,$$

namely $\Omega=d\log z_{0}\wedge\frac{dz_{1}\wedge dz_{2}}{z_{3}}$. This model has a natural $T^{2}$-symmetry: one $S^{1}$ acts trivially on $z_{1},z_{2},z_{3}$ and rotates $z_{0}$, while the other $S^{1}$ acts trivially on $z_{0},z_{3}$ and diagonally on $z_{1},z_{2}$. The model is intimately related to the Ooguri-Vafa metric (cf. Section 1.3.2), and we expect this region to coincide with the neighbourhood of edges in the Gross-Ruan-Joyce picture.