Complex sentence: In particular, a Miller index is determined by three integers\\ ell, m, n, the Miller indices, and is written (\\ ell m n) for a plane and (\\ ell m n) for a direction perpendicular to the plane.
Split into simpler sentences: In particular, a plane or direction is determined by three integers\\ ell, m, and n, the "Miller indices". They are written (\\ ell m n) for a plane and (\\ ell m n) for a direction perpendicular to the plane.