<Dd> h + k + i = 0 . </Dd> <P> Here h, k and l are identical to the corresponding Miller indices, and i is a redundant index . </P> <P> This four - index scheme for labeling planes in a hexagonal lattice makes permutation symmetries apparent . For example, the similarity between (110) ≡ (11 20) and (120) ≡ (1210) is more obvious when the redundant index is shown . </P> <P> In the figure at right, the (001) plane has a 3-fold symmetry: it remains unchanged by a rotation of 1 / 3 (2π / 3 rad, 120 °). The (100), (010) and the (110) directions are really similar . If S is the intercept of the plane with the (110) axis, then </P>

What is the importance of miller indices in crystallography