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Minerals are three‐dimensional Earth materials with three‐dimensional crystal lattices. The fundamental units of pattern in any three‐dimensional lattice are three‐dimensional motifs that can be classified according to their translation‐free symmetries. These three‐dimensional equivalents of the two‐dimensional plane point groups are called space point groups.

Space point groups can be represented by nodes. These nodes can be translated to produce three‐dimensional patterns of points called space lattices. Space lattices are the three‐dimensional equivalents of plane nets or meshes. By analogy with unit meshes or nets, we can recognize the smallest three‐dimensional units, called unit cells, which contain all the information necessary to produce the three‐dimensional space lattices. In this section, we will briefly describe the space point groups, after which we will introduce Bravais lattices, unit cells, and their relationship to the six (or seven) major crystal systems to which minerals belong.

Figure 4.10 A primitive unit cell and a long‐range space point lattice that results from its repetition by symmetry operations in three dimensions.