International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B. ch. 2.1, p. 193

Table 2.1.3.3 

U. Shmuelia* and A. J. C. Wilsonb

aSchool of Chemistry, Tel Aviv University, Tel Aviv 69 978, Israel, and bSt John's College, Cambridge, England
Correspondence e-mail:  ushmueli@post.tau.ac.il

Table 2.1.3.3| top | pdf |
Average multiples for the 32 point groups (modified from Rogers, 1950[link]).

The multiple gives [S/\Sigma] for the row and zone corresponding to the principal axis of the point-group symbol; those for the secondary and tertiary axes are given when the symbol contains such axes.

Point groupPrincipalSecondaryTertiary
RowZoneRowZoneRowZone
1 1 1        
[\bar{1}] 1 1        
2 2 1        
m 1 2        
[2/m] 2 2        
222 2 1 2 1 2 1
mm2 2 2 2 2 4 1
mmm 4 2 4 2 4 2
4 4 1        
[\bar{4}] 2 1        
[4/m] 4 2        
422 4 1 2 1 2 1
4mm 8 1 2 2 2 2
[\bar{4}2m] 4 1 2 1 2 2
[4/mmm] 8 2 4 2 4 2
3 3 1        
[\bar{3}] 3 1        
321 3 1 2 1 1 1
3m1 6 1 1 2 2  
31m 6 1 2 2 2 1
6 6 1        
[\bar{6}] 3 2        
[6/m] 6 2        
622 6 1 2 1 2 1
6mm 12 1 2 2 2 2
[\bar{6}m2] 6 2 2 2 4 1
[6/mmm] 12 2 4 2 4 2
231 2 1 3 1 1 1
[m\bar{3}1] 4 2 3 1 1 1
432 4 1 3 1 2 1
[\bar{4}3m] 4 1 6 1 2 2
[m\bar{3}m] 8 2 6 2 4 2

Note. The pairs of point groups, 1 and [\bar{1}] and 3 and [\bar{3}], not distinguished by average multiples, may be distinguished by their centric and acentric probability density functions.
The entry for the principal zone for the point group 422 was given incorrectly as 2 in the first edition of this volume.