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For example, rhombohedral primitive cell for an FCC is defined as:

a_1 = 1/2 a*(x+y);

a_2=1/2*a(y+z);

a_3=1/2*a(z+x);

If we have a plane, for example the 111 plane on an FCC, how do we describe this for a rhombodial primitive cell?

I have no clue how to do this, i tried finding a constant to multiple a_1,a_2 and a_3 for example to the normal vector on the 111 plane [1,1,1], but i got something i don't think is right.

Could someone point me in the right direction, or a link to an explanation?

thanks,