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

International Tables for Crystallography (2016). Vol. A, ch. 3.1, p. 701

Table 3.1.2.1 

H. Burzlaffa and H. Zimmermannb

Table 3.1.2.1| top | pdf |
Two-dimensional Bravais types of lattices

Bravais type of latticeLattice parametersMetric tensorProjections
ConventionalPrimitiveConventionalPrimitive/transformation to primitive cellRelations of the components
mp a, b a, b [\matrix{g_{11} &g_{12}\hfill\cr &g_{22}\hfill\cr}] [\matrix{g_{11} &g_{12}\hfill\cr &g_{22}\hfill\cr}]   [Scheme scheme130]
γ γ
op a, b a, b [\matrix{g_{11} &0\hfill\cr &g_{22}\hfill\cr}] [\matrix{g_{11} &0\hfill\cr &g_{22}\hfill\cr}]   [Scheme scheme131]
γ = 90° γ = 90°
oc a1 = a2, γ P(c) [g'_{11} = {\textstyle{1 \over 4}}(g_{11} + g_{22})] [Scheme scheme132]
  [\matrix{g'_{11} &g'_{12}\hfill\cr &g'_{11}\hfill\cr}] [g'_{12} = {\textstyle{1 \over 4}}(g_{11} - g_{22})]
[g_{11} = 2(g'_{11} + g'_{12})]
[g_{12} = 2(g'_{11} - g'_{12})]
tp a1 = a2 a1 = a2 [\matrix{g_{11} &0\hfill\cr &g_{11}\hfill\cr}] [\matrix{g_{11} &0\hfill\cr &g_{11}\hfill\cr}]   [Scheme scheme133]
γ = 90° γ = 90°
hp a1 = a2 a1 = a2 [\matrix{g_{11} &-{\textstyle{1 \over 2}}\,g_{11}\hfill\cr &\phantom{-{\textstyle{1 \over 2}}\,}g_{11}\hfill\cr}] [\matrix{g_{11} &-{\textstyle{1 \over 2}}\,g_{11}\hfill\cr &\phantom{-{\textstyle{1 \over 2}}\,}g_{11}\hfill\cr}]   [Scheme scheme134]
γ = 120° γ = 120°
The symbols for Bravais types of lattices were adopted by the International Union of Crystallography in 1985; cf. de Wolff et al. (1985[link]).
[{\bi P}(c) =\textstyle{1 \over 2}(11/\bar{1}1).]