Drawing lattice planes

Just as you do when indexing a plane, it is necessary to choose the correct point of reference from which to work.

Taking the conventional origin at the far bottom left of the unit, we can then move along to the next lattice point in the x, y or z directions.

If you have a negative h index move the point of reference along the x-axis to the other side of the unit cell, so that you can then go back in the negative x direction to find your intercept. Do the same for negative k and l indices.

To draw the (122) plane, go back to -a on the x-axis.

go along to b/2 on the y-axis

and go up to c/2 on the z-axis.

We can join these points to mark the trace of the plane on the unit cell surface, and then fill in the plane.