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4.4 THREE‐DIMENSIONAL MOTIFS AND LATTICES
three‐dimensional motifsspace point groups
space lattices
ssss1 A primitive unit cell and a long‐range space point lattice that results from its repetition by symmetry operations in three dimensions.
4.4.1 Space point groups
In minerals, the fundamental motifs are parts of clusters of three‐dimensional coordination polyhedra sufficient to establish the composition of the mineral. When these are repeated in three dimensions during mineral growth, they produce the long‐range order characteristic of crystalline substances (ssss1). Like all fundamental units of pattern, these three‐dimensional motifs can be classified on the basis of their translation‐free symmetries.
32 space point groups32 crystal classes
4.4.2 Bravais lattices, unit cells, and crystal systems
abc
unit cellabcprimitive (P)Non‐primitive cells
Unit cells bear a systematic relationship to the coordination polyhedra and packing of atoms that characterize mineral structures, as illustrated by ssss1.