I am looking for references on eigenfunctions with Neumann boundary condition. 

In an article, the author wrote in introduction that when a domain is planar polygon, the second eigenfunctions on it have critical points at vertices. But, I could not find the source. I think this is probably a well-known fact. But I am very interested in the proof.

 It may be a famous fact for experts, but I would appreciate it if you could tell me.