Let $K$ be a simplicial complex in $R^2$ such that $|K|$ is a simple polygon with inside. An internal edge $ab \in K$ is an edge such that both of its two endpoints a and b are NOT on the boundary of $|K|$. Prove or disprove that:
link($ab$) = link($a$) $\cap$ link($b$)
Does anyone know how to prove it or disprove it? I am new to simplicial complex, can you guide me to do it?