Continuing with Example 7.2, the dual intersection complex is the boundary of a tetrahedron, with each face affine isomorphic to a standard two-simplex, and the affine structure near each vertex makes the polyhedral decomposition look locally like the fan for $\mathbb{P}^{2}$. There is one singularity at the barycenter of each edge, and one can calculate that the monodromy of $\Lambda$ about each of these singularities is $\begin{pmatrix}1&4\\ 0&1\end{pmatrix}$ in a suitable basis.