Take reciprocals of intercepts and clear fractions.
Miller indices (hkl) describe the orientation of crystal planes. To find them: (1) Determine where the plane intercepts the crystallographic axes (in units of a, b, c). (2) Take the reciprocals. (3) Clear fractions to get the smallest integers. A plane parallel to an axis has intercept ∞, giving index 0. For cubic crystals, the d-spacing (distance between parallel planes) is d = a/√(h²+k²+l²), which is essential for X-ray diffraction via Bragg's law: nλ = 2d sin θ. Common planes: (100) faces of a cube, (110) diagonal faces, (111) body diagonals. Miller indices are used in materials science, semiconductor fabrication (silicon wafer orientations), and mineralogy to describe crystal faces and cleavage planes.