, then $\mathrm{stab}(J_0) \cap \mathrm{stab}(J_0)$ is conjugate to $\langle G_u,G_v \rangle$ for some adjacent vertices $u,v \in V(\Gamma)$.  -   If $J_0$ and $J_0$ are not transverse and if there exists a third hyperplane $J$ transverse to both $J_0$ and $J_0$, then $\mathrm{stab}(J_0) \cap \mathrm{stab}(J_0)$ is conjugate to $G_u$ for some vertex $u \in V(\Gamma)$.  -   If $J_0$ and $J_0$ are not transverse and if no hyperplane is transverse to both $J_0$ and $J_0$, then $\mathrm{stab}(J_0) \cap \mathrm{stab}(J_0)$ is 