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motifsymmetry operationsnode

Simple symmetry operationsCompound symmetry operations

translationunit translation vector (t)

Two‐dimensional translationstwo unit translation vectorstaand tbt1and t2a1b2plane latticeplane mesh

1212123

Three‐dimensional translationsthree unit translation vectorsta, tb, and tct1, t2, and t3a1b2c3space latticecrystal lattice

ssss1 Five major types of rotational symmetry operations, viewed looking down rotational axes marked by blue symbols in the center of each circle: dot marks axis of onefold rotation (1), oval marks axis of twofold rotation (2), triangle marks axis of threefold rotation (3), square marks axis of fourfold rotation (4), and hexagon marks axis of sixfold rotation (6).

Rotation (n)axis of rotation (A)

ssss1 Five common axes of rotational symmetry in minerals.

Type Symbolic notation Description Onefold axis of rotation 1 Any axis of rotation about which the motif is repeated only once during a 360° rotation (ssss1 (1)) Twofold axis of rotation 2 Motifs repeated every 180° or twice during a 360° rotation (ssss1 (2)) Threefold axis of rotation 3 Motifs repeated every 120° or three times during a complete rotation (ssss1 (3)) Fourfold axis of rotation 4 Motifs repeated every 90° or four times during a complete rotation (ssss1 (4)) Sixfold axis of rotation 6 Motifs repeated every 60° or six times during a complete rotation (ssss1 (5))