Hi harkiranjeet kaur,
According to your first question (as far as I can understand it), the main difference between Hexagonal photonic lattice and Triangular lattice is the geometry of the molecular lattice structure which lays beyond it. This lattice geometry can be observed with the respect to a virtual plane perpendicular to the main optical axis. According to your second question, I don’t have a lot of experience in modeling triangular lattice in OptiFDTD, so I won’t be able to give you a good advice.