Table 2.1.3.3

Shmueli, U.; Wilson, A. J. C.

doi:10.1107/97809553602060000554

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

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

Table 2.1.3.3

U. Shmueli^a ^* and A. J. C. Wilson^b ^‡

^a School 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).

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 group	Principal		Secondary		Tertiary
Point group	Row	Zone	Row	Zone	Row	Zone
1	1	1
$[\bar{1}]$	1	1
2	2	1
m	1	2
	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	2
422	4	1^†	2	1	2	1
4mm	8	1	2	2	2	2
$[\bar{4}2m]$	4	1	2	1	2	2
	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	2
622	6	1	2	1	2	1
6mm	12	1	2	2	2	2
$[\bar{6}m2]$	6	2	2	2	4	1
	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.