Hello, sorry to bother again but I've been giving this much thought as well and am very confused.. Please refer to the following page: http://x5.freeshare.us/119fs641427.jpg If I am supposed to calculate the direction vector for the hexagonal crystal, I was told to: 1) Calculate the line of projection of the vector (from origin to X) onto the base plane 2) Calculate the new line of projection of this projected line with respect to a1 and a2 axis. 3) Reduce the ratio of a1: a2 to the lowest integer 4) Calculate the line of projection of the vector onto the verticle z axis 5) Use the 3-index system to 4-index system formula to convert it and eventually get [11 (-2) 1] for the mentioned vector. However, this would imply that the z vector is independent of the ratio in a1 and a2 since using this method we would have gotten 0.5 unit length for a1 and a2 and 1 unit length for z. If not, shouldn't it be [11 (-2) 2] instead? I'm sorry if I sound confusing, because I'm very confused myself as well. But if anyone knows about this, please help, thanks!