System  Class  Polar (symmetry) axes  Nonpolar directions 
Triclinic 
1 
None^{†} 
None 
Monoclinic 
2 
[010] 
[u0w] 
Unique axis b 
m 
None^{†} 
[010] 
Monoclinic 
2 
[001] 
[uv0] 
Unique axis c 
m 
None^{†} 
[001] 
Orthorhombic 
222 
None 
[0vw]; [u0w]; [uv0] 
mm2 
[001] 
[uv0] 
Tetragonal 
4 
[001] 
[uv0] 

None 
[001]; [uv0] 
422 
None 
[uv0]; [0vw] [u0w]; 


[uuw] [] 
4mm 
[001] 
[uv0] 

None 
[uv0]; [0vw] [u0w] 

None 
[uv0]; [uuw] [] 
Trigonal
(Hexagonal axes) 
3 
[001] 
None 
321 
[100], [010], 
[u2uw] 
312 
, [120], 
[uuw] 
3m1 
[001] 
[100] [010] 
31m 
[001] 
[120] 
Trigonal
(Rhombohedral axes) 
3 
[111] 
None 
32 
, , 
[uuw] [uvv] [uvu] 
3m 
[111] 

Hexagonal 
6 
[001] 
[uv0] 

None 
[001] 
622 
None 
[u2uw] [] 


[uuw] [] 
6mm 
[001] 
[uv0] 

, [120], 
[uuw] [] 

[100], [010], 
[u2uw] 
Cubic 



432 


^{†}In class 1 any direction is polar; in class m all directions except [010] (or [001]) are polar.
