Crystallographic symmetry elements—zones and zone axes, center of symmetry (i), mirror planes (m), and rotation axes (n)—describe the geometric regularity of crystals and are fundamental for classifying crystal systems.
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THE REPETITION THEORY
Crystallography is fundamentally based on periodic atomic repetition governed by symmetry elements—translation, rotation, reflection, inversion, and their combinations—which determine crystal structures and their 1D, 2D, and 3D patterns.
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CRYSTALLOGRAPHIC PROJECTION
Crystallographic projection converts a crystal’s 3D form into 2D representations—through spherical, gnomonic, orthographic, and especially stereographic projections—to analyze crystal face orientation and symmetry.
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CRYSTAL 3: Weiss Coefficients and Miller Indices
Weiss coefficients describe crystal planes by their axis intercept ratios, while Miller indices use their reciprocals (hkl) to give rational, integer-based plane designations without infinite values.
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