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

International Tables for Crystallography (2015). Vol. A, ch. 1.4, p. 45

Table 1.4.1.1 

H. Wondratscheke

Table 1.4.1.1| top | pdf |
The structure of the Hermann–Mauguin symbols for the space groups

The positions of the representative symmetry directions for the different crystal systems are given. The description of the non-translational part of the HM symbol is always preceded by the lattice symbol, which in conventional settings is P, A, B, C, F, I or R. For monoclinic b setting and monoclinic c setting, cf. Section 1.4.1.4.4[link]; the primitive hexagonal lattice is called H in this table.

Crystal system First positionSecond positionThird position
Triclinic (anorthic)   1 or [\bar{1}]
Monoclinic b setting 1 b 1
Monoclinic c setting 1 1 c
Orthorhombic a b c
Tetragonal c a ab
Trigonal H lattice c a 1
    or  
  c 1 ab
Trigonal, R lattice, hexagonal coordinates [{\bf c}_H] [{\bf a}_H]
    or  
Trigonal, R lattice, rhombohedral coordinates [{\bf a}_R+{\bf b}_R+{\bf c}_R] [{\bf a}_R-{\bf b}_R]
Hexagonal c a ab
Cubic c [{\bf a}+{\bf b}+{\bf c}] ab