Hi every one I have a question regarding the k-points and I was wondering if any one can guide me in the right path. At present I am writing a software in which I am trying to design a photonic crystal structure. I want this photonic structure to produce the same DISPERSION DIAGRAM as a natural NaCl crystal. So simply put I am trying to produce an artificial crystal which produces the same results as a natural crystal. I've looked into the concepts of Brillouin zone and k-points but I can not get the big picture in my head to combine it with photonics. As we know NaCl is a FCC crystal. So my questions are: 1: How would you determine its critical points? Would it be e.g. GKLX or GMKG as I've attached the images with this question? (P.s. the examples that I've mentioned are not for NaCl and are just examples). 2: Once you determine the critical points, what would be the shape of the k-points? As you can see in this picture the first Brillouin zone is the red hexagonal but the k-points are GMK in the green triangle. How was this triangle shape determined? Because if I have a much more complex structure what would I expect the k-points to be look like? What would also NaCl look like? That's all. Thank you in advance and any help would be appreciated.