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. 151

Table 2.1.3.1 

Th. Hahna and A. Looijenga-Vosb

Table 2.1.3.1| top | pdf |
Lattice symmetry directions for two and three dimensions

Directions that belong to the same set of equivalent symmetry directions are collected between braces. The first entry in each set is taken as the representative of that set.

LatticeSymmetry direction (position in Hermann–Mauguin symbol)
PrimarySecondaryTertiary
Two dimensions
Oblique [\matrix{\hbox{Rotation}\hfill\cr \hbox{point}\hfill\cr\hbox{in plane}\hfill\cr}]    
Rectangular [10] [01]
Square [\left\{\matrix{[10]\cr [01]\cr}\right\}] [\left\{\matrix{[1\bar{1}]\cr [11]\cr}\right\}]
Hexagonal [\left\{\matrix{[10]\cr [01]\cr [\bar{1}\bar{1}]\cr}\right\}] [\left\{\matrix{[1\bar{1}]\cr [12]\cr [\bar{2}\bar{1}]\cr}\right\}]
Three dimensions
Triclinic None    
Monoclinic [010] (`unique axis b')  
  [001] (`unique axis c')  
Orthorhombic [100] [010] [001]
Tetragonal [001] [\left\{\matrix{[100]\cr [010]\cr}\right\}] [\left\{\matrix{[1\bar{1}0]\cr [110]\cr}\right\}]
Hexagonal [001] [\left\{\matrix{[100]\cr [010]\cr [\bar{1}\bar{1}0]\cr}\right\}] [\left\{\matrix{[1\bar{1}0]\cr [120]\cr [\bar{2}\bar{1}0]\cr}\right\}]
Rhombohedral (hexagonal axes) [001] [\left\{\matrix{[100]\cr [010]\cr [\bar{1}\bar{1}0]\cr}\right\}]  
Rhombohedral (rhombohedral axes) [111] [\left\{\matrix{[1\bar{1}0]\cr [01\bar{1}]\cr [\bar{1}01]\cr}\right\}]  
Cubic [\left\{\matrix{[100]\cr [010]\cr [001]\cr}\right\}] [\left\{\matrix{[111]\cr [1\bar{1}\bar{1}]\cr [\bar{1}1\bar{1}]\cr [\bar{1}\bar{1}1]\cr}\right\}] [\left\{\matrix{[1\bar{1}0]\ [110]\cr [01\bar{1}]\ [011]\cr [\bar{1}01]\ [101]\cr}\right\}]
For the full Hermann–Mauguin symbols see Sections 2.1.3.4[link] and 1.4.1[link] .