International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 2.1, pp. 165-166

## Table 2.1.3.7

Th. Hahna and A. Looijenga-Vosb
 Table 2.1.3.7| top | pdf | Zonal and serial reflection conditions for glide planes and screw axes (cf. Table 2.1.2.1)
 (a) Glide planes
Type of reflectionsReflection conditionGlide planeCrystallographic coordinate system to which condition applies
Orientation of planeGlide vectorSymbol
0kl (100) b
c
n
d
h0l (010) c
a
n
d
hk0 (001) a
b
n
d
c
c
c, n
d
a, n
d
b, n
d
 (b) Screw axes
Type of reflectionsReflection conditionsScrew axisCrystallographic coordinate system to which condition applies
Direction of axisScrew vectorSymbol
h00 [100]
0k0 [010]
00l [001]
000l [001]
Glide planes d with orientations (100), (010) and (001) occur only in orthorhombic and cubic F space groups. Combination of the integral reflection condition (hkl: all odd or all even) with the zonal conditions for the d glide planes leads to the further conditions given between parentheses.
For rhombohedral space groups described with `rhombohedral axes', the three reflection conditions imply interleaving of c and n glides, a and n glides, and b and n glides, respectively. In the Hermann–Mauguin space-group symbols, c is always used, as in R3c (161) and , because c glides also occur in the hexagonal description of these space groups.
§For tetragonal P space groups, the two reflection conditions (hhl and with ) imply interleaving of c and n glides. In the Hermann–Mauguin space-group symbols, c is always used, irrespective of which glide planes contain the origin: cf. P4cc (103), and .
For cubic space groups, the three reflection conditions imply interleaving of c and n glides, a and n glides, and b and n glides, respectively. In the Hermann–Mauguin space-group symbols, either c or n is used, depending upon which glide plane contains the origin, cf. , , versus , , .