Why do some sources list six crystal systems while others list seven?

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The classification of crystals into either six or seven systems depends on how the hexagonal system is categorized.

While crystals are generally grouped into six primary systems based on their symmetry elements and crystallographic axes—isometric, hexagonal, tetragonal, orthorhombic, monoclinic, and triclinic—many sources distinguish seven systems by separating the trigonal system from the hexagonal system.12

This distinction arises because the trigonal system, which is sometimes referred to as the rhombohedral system, possesses a threefold rotation axis that can be grouped separately from the sixfold symmetry characteristic of the hexagonal system. Both classifications are used in crystallography to organize the 32 possible crystal classes based on their internal atomic arrangements and symmetry.132