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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 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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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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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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Crystals are orderly solids formed by magma cooling and are classified into seven systems based on axis lengths and angles.
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Nicolaus Steno’s Law states that a mineral always has constant interfacial angles, measurable with goniometers or X-ray diffraction.
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