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

International Tables for Crystallography (2016). Vol. A, ch. 2.1, p. 143

Table 2.1.1.1 

Th. Hahna and A. Looijenga-Vosb

Table 2.1.1.1| top | pdf |
Crystal families, crystal systems, conventional coordinate systems and Bravais lattices in one, two and three dimensions

Crystal familySymbolCrystal systemCrystallographic point groupsNo. of space groupsConventional coordinate systemBravais lattices
Restrictions on cell parametersParameters to be determined
One dimension
[Scheme scheme1] 2 None a [{\scr p}]
Two dimensions
Oblique m Oblique [Scheme scheme2] 2 None a, b mp
(monoclinic)         γ§  
Rectangular o Rectangular [Scheme scheme3] 7 [\gamma = 90^{\circ}] a, b op
(orthorhombic)           oc
Square t Square [Scheme scheme4] 3 [a = b] a tp
(tetragonal)       [\gamma = 90^{\circ}]    
Hexagonal h Hexagonal [Scheme scheme5] 5 [a = b] a hp
        [\gamma = 120^{\circ}]    
Three dimensions
Triclinic a Triclinic [Scheme scheme6] 2 None [a,b,c] aP
(anorthic)         [\alpha, \beta, \gamma]  
Monoclinic m Monoclinic [Scheme scheme7] 13 b-unique setting [a,b,c] mP
        [\alpha = \gamma = 90^{\circ}] β § mS (mC, mA, mI)
        c-unique setting [a, b, c] mP
        [\alpha = \beta = 90^{\circ}] γ § mS (mA, mB, mI)
Orthorhombic o Orthorhombic [Scheme scheme8] 59 [\alpha = \beta = \gamma = 90^{\circ}] a, b, c oP
oS (oC, oA, oB)
oI
oF
Tetragonal t Tetragonal [Scheme scheme9] 68 [a = b] a, c tP
        [\alpha = \beta = \gamma = 90^{\circ}]   tI
Hexagonal h Trigonal [Scheme scheme10] 18 [a = b] a, c hP
        [\alpha = \beta = 90^{\circ},\ \gamma = 120^{\circ}]    
      7 [a = b = c] [\alpha = \beta = \gamma] (rhombohedral axes, primitive cell) [a = b] [\alpha = \beta = 90^{\circ}, \gamma = 120^{\circ}] (hexagonal axes, triple obverse cell) a, α hR
    Hexagonal [Scheme scheme11] 27 [a = b] a, c hP
        [\alpha = \beta = 90^{\circ}, \gamma = 120^{\circ}]    
Cubic c Cubic [Scheme scheme12] 36 [a = b = c] a cP
        [\alpha = \beta = \gamma = 90^{\circ}]   cI
            cF
The symbols for crystal families (column 2) and Bravais lattices (column 8) were adopted by the International Union of Crystallography in 1985; cf. de Wolff et al. (1985)[link].
Symbols surrounded by dashed or full lines indicate Laue groups; full lines indicate Laue groups which are also lattice point symmetries (holohedries).
§These angles are conventionally taken to be non-acute, i.e. [\geq 90^{\circ}].
For the use of the letter S as a new general, setting-independent `centring symbol' for monoclinic and orthorhombic Bravais lattices, see de Wolff et al. (1985)[link].