Vertex link of a Salvetti complex
= Vertex link of a Salvetti complex
The unique vertex of $S_\Gamma$ has two link vertices $v^+,v^-$ for each $v\in V(\Gamma)$. Signed vertices $v_1^{\epsilon_1},\ldots,v_k^{\epsilon_k}$ span a simplex exactly when the distinct underlying vertices $v_1,\ldots,v_k$ form a clique of $\Gamma$.