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Source: Wenk and Bulakh (2016). © Cambridge University Press.

ssss1 The 14 Bravais lattices and the six (or seven) crystal systems they represent.

Source: Courtesy of Steve Dutch.

ssss1 Major characteristics of Bravais lattice cells in the major crystal systems.

Crystal system Unit cell edge lengths Unit cell edge intersection angles Bravais lattice types Isometric (cubic) 123 α = β = γ = 90° Primitive (P) Body centered (I) Face centered (F) Tetragonal 123 α = β = γ = 90° Primitive (P) Body centered (I) Hexagonal (hexagonal) 12 ≠ (α = β = 90^o ≠ γ = 120°) Primitive (P) Hexagonal (trigonal or rhombohedral) 123 α = β = γ ≠ 90° Primitive (P) Orthorhombic a ≠ b ≠ c (α = β = γ = 90°) Primitive (P) Body centered (I) End centered (A, B, C) Face centered (F) Monoclinic a ≠ b ≠ c (α = γ = 90° ≠ β) Primitive (P) End centered (C) Triclinic a ≠ b ≠ c (α, β, and γ ≠ 90°) Primitive (P)

Imagine yourself, if you can, the crystals on a web site, in a mineral shop or a museum. Such crystals are partially or completely bounded by planar crystal faces that are produced when minerals grow. Many other mineral specimens are partially or completely bounded by flat, planar cleavage faces produced when minerals break along planes of relatively low total bond strength. The shapes of the crystals, the number and orientation of the crystal faces, and the nature of the cleavage depend on the crystal structure of the mineral. That is, they depend on the basic motif and the symmetry operations that produce the three‐dimensional crystal lattice. The nature of the crystal forms and cleavage surfaces depends on the crystal system and crystal class in which the mineral crystallized.