Evolution is the gradual change in inherited traits within populations over time—shaped by genetics, natural selection, and environmental pressures—studied through taxonomy and evidenced in fossils by morphological changes that lead to adaptation, speciation, and extinction.
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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 SYMMETRY ELEMENTS
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
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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