Earth Materials. John O'Brien

i, 1A₆, 6A₂, 7m Ditrigonal–dipyramidal 6m2 1A₆, 3A₂, 3m Dihexagonal–pyramidal 6mm 1A₆, 6m Hexagonal–trapezohedral 622 1A₆, 6A₂ Hexagonal–dipyramidal 6/m i, 1A₆, 1m Trigonal–dipyramidal Hexagonal–pyramidal 6 1A₆ Hexagonal (rhombohedral or trigonal) Hexagonal–scalenohedral , 3A₂, 3m Ditrigonal–pyramidal 3m 1A₃, 3m Trigonal–trapezohedral 32 1A₃, 3A₂ Rhombohedral Trigonal–pyramidal 3 1A₃ Orthorhombic Rhombic–dipyramidal 2/m2/m2/m i, 3A₂, 3m Rhombic–pyramidal mm2 1A₂, 2m Rhombic–disphenoidal 222 3A₂ Monoclinic Prismatic 2/m i, 1A₂, 1m Sphenoidal 2 1A₂ Domatic m 1m Triclinic Pinacoidal i Pedial 1 None

Figure 4.11 Relationship between (a) atomic packing, (b) a unit cell, and (c) octahedral coordination polyhedra in halite (NaCl).

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

Figure 4.12 The 14 Bravais lattices and the six (or seven) crystal systems they represent.

      Source: Courtesy of Steve Dutch.

Table 4.4 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)	(a = b = c) Preferred format for edges of equal length is (a1 = a2 = a3)	α = β = γ = 90°	Primitive (P) Body centered (I) Face centered (F)
Tetragonal	(a1 = a2 ≠ a3) or a = b ≠ c	α = β = γ = 90°	Primitive (P) Body centered (I)
Hexagonal (hexagonal)	(a1 = a2 ≠ c) (a = b ≠ c)	(α = β = 90o ≠ γ = 120°)	Primitive (P)
Hexagonal (trigonal or rhombohedral)	(a1 = a2 = a3)	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)

4.5 CRYSTAL SYSTEMS

      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,