Lens spaces as dual complexes of Log Calabi-Yau pairs

We demonstrate the construction of singular log Calabi-Yau $4$-folds such that the dual complex of the boundary is homeomorphic to a Lens space from a log Calabi-Yau surface with action of a finite cyclic group. We explicitly obtain the Lens spaces $L(3,1)$, $L(5,1)$, and $L(5,2)$ in this way.