Solution
= Solution
The <hyperplane of a Salvetti complex> dual to the loop labelled $v$ is itself the Salvetti complex of the <induced subgraph> on the neighbours of $v$. If this hyperplane were homeomorphic to a closed surface, its vertex link would be a cycle. Part (c), applied to that induced graph, says that the graph must be one edge. Its Salvetti complex is therefore the two-dimensional <torus>, a surface of genus one. It cannot be a <closed orientable surface> of genus two.