International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by Th. Hahn

International Tables for Crystallography (2006). Vol. A, ch. 4.2, p. 61

Section 4.2.1. Arrangement of the tables

E. F. Bertauta

aLaboratoire de Cristallographie, CNRS, Grenoble, France

4.2.1. Arrangement of the tables

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Comparative tables for the 17 plane groups first appeared in IT (1952)[link]. The classification of plane groups is discussed in Chapter 2.1[link] . Table 4.2.1.1[link] lists for each plane group its system, lattice symbol, point group and the plane-group number, followed by the short, full and extended Hermann–Mauguin symbols. Short symbols are included only where different from the full symbols. The next column contains the full symbol for another setting which corresponds to an interchange of the basis vectors a and b; it is only needed for the rectangular system. Multiple cells c and h for the square and the hexagonal system are introduced in the last column.

Table 4.2.1.1| top | pdf |
Index of symbols for plane groups

System and lattice symbolPoint groupNo. of plane groupHermann–Mauguin symbolFull symbol for other settingMultiple cell
ShortFullExtended
Oblique 1   1   p1      
p 2   2   p2      
Rectangular
p, c
m [\Bigg\{] 3 pm [p1m1]   [p11m]  
4 pg [p1g1]   [p11g]  
5 cm [c1m1] [\matrix{c1m1\hfill\cr g\hfill\cr}] [c11m]  
2mm [\Bigg\{] 6   [p2mm]   [p2mm]  
7   [p2mg]   [p2gm]  
8   [p2gg]   [p2g g]  
9   [c2mm] [\matrix{c2mm\hfill\cr g\ g\hfill\cr}] [c2mm]  
Square
p
4   10   [p4]     [c4]
4mm [\Bigg\{] 11   [p4mm] [\matrix{p4mm\hfill\cr g\hfill\cr}]   [\matrix{c4mm\hfill\cr g\hfill\cr}]
12   [p4gm] [\matrix{p4gm\hfill\cr g\hfill\cr}]   [\matrix{ c4mg\hfill\cr g\hfill\cr}]
Hexagonal
p
3   13   p3     h3
3m [\Bigg\{] 14   [p3m1] [\matrix{p3m1\hfill\cr g\hfill}]   [\matrix{h31m\hfill\cr g\hfill\cr}]
15   [p31m] [\matrix{p31m\hfill\cr g\hfill\cr}]   [\matrix{ h3m1\hfill\cr g\hfill\cr}]
6   16   p6     h6
6mm   17   p6mm [\matrix{p6mm\hfill\cr g\;g\hfill\cr}]   [\matrix{h6mm\hfill\cr g\;g\hfill\cr}]

References

International Tables for X-ray Crystallography (1952). Vol. I, edited by N. F. M. Henry & K. Lonsdale. Birmingham: Kynoch Press. [Abbreviated as IT (1952).]








































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