I know how to calculate Miller indices (hkl), but I have found a weird one I can not work out could you please help, I know your you have to expand the plane but after that I’m lost.
$\begingroup$ See also: chemistry.stackexchange.com/q/82937 $\endgroup$– Karsten ♦Mar 31, 2022 at 17:10
Because of translational symmetry, every plane has a set of symmetry-equivalent parallel planes (infinitely many). To get the Miller indexes, you have to find the plane closest to the origin that does not pass through the origin. The example shows a plane that goes through the origin. If you translate it by -b, it will cross a at 1/2, b at -1 and c at -1. So it is the 2, -1, -1 plane, also known as -2, 1, 1.