International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 3.1, pp. 702-703

Table 3.1.2.2

H. Burzlaffa and H. Zimmermannb
 Table 3.1.2.2| top | pdf | Three-dimensional Bravais types of lattices
Bravais type of latticeLattice parametersMetric tensorProjections
ConventionalPrimitiveConventionalPrimitive/transf.Relations of the components
aP a, b, c a, b, c
α, β, γ α, β, γ
mP a, b, c a, b, c
β, α = γ = 90° β, α = γ = 90°
mC a1 = a2, c P(C)
(mS) γ, α = β

oP a, b, c a, b, c
α = β = γ = 90° α = β = γ = 90°
oC a1 = a2, c P(C)
(oS) γ, α = β = 90°

oI a1 = a2 = a3 P(I)
α, β, γ
cos α + cos β + cos γ = −1

oF a, b, c
α, β, γ

tP a1 = a2, c a1 = a2, c
α = β = γ = 90° α = β = γ = 90°
tI a1 = a2 = a3
γ, α = β
2 cos α + cos γ = −1

hR a1 = a2, c a1 = a2 = a3
α = β = 90° α = β = γ
γ = 120°
hP a1 = a2, c
α = β = 90°
γ = 120°
cP a1 = a2 = a3 a1 = a2 = a3
α = β = γ = 90° α = β = γ = 90°
cI a1 = a2 = a3 P(I)
α = β = γ = 109.5°
cF a1 = a2 = a3 P(F)
α = β = γ = 60°
The symbols for Bravais types of lattices were adopted by the International Union of Crystallography in 1985; cf. de Wolff et al. (1985). Symbols in parentheses are standard symbols, see Table 2.1.1.1 .