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

International Tables for Crystallography (2016). Vol. A, ch. 2.1, p. 145

## Table 2.1.2.1

Th. Hahna and M. I. Aroyoc
 Table 2.1.2.1| top | pdf | Symbols for symmetry elements and for the corresponding symmetry operations in one, two and three dimensions
SymbolSymmetry element and its orientationDefining symmetry operation with glide or screw vector
m Reflection plane, mirror plane Reflection through the plane
Reflection line, mirror line (two dimensions) Reflection through the line
Reflection point, mirror point (one dimension) Reflection through the point
a, b or c Axial' glide plane Glide reflection through the plane, with glide vector
a or
b or
c or
or
e Double' glide plane (in centred cells only) Two glide reflections through one plane, with perpendicular glide vectors
and
and
and
; and ; and
; and ; and
; and ; and
n Diagonal' glide plane Glide reflection through the plane, with glide vector
; ; ; ;
or or
; ; ; ;
d § Diamond' glide plane Glide reflection through the plane, with glide vector
; ; ; ;
; ; ; ;
; ; ; ;
g Glide line (two dimensions) Glide reflection through the line, with glide vector
; ;
1 None Identity
2, 3, 4, 6 n-fold rotation axis, n Counter-clockwise rotation of degrees around the axis
n-fold rotation point, n (two dimensions) Counter-clockwise rotation of degrees around the point
Centre of symmetry, inversion centre Inversion through the point
, Rotoinversion axis, , and inversion point on the axis †† Counter-clockwise rotation of degrees around the axis, followed by inversion through the point on the axis ††
n-fold screw axis, Right-handed screw rotation of degrees around the axis, with screw vector (pitch) () t; here t is the shortest lattice translation vector parallel to the axis in the direction of the screw
In the rhombohedral space-group symbols (161) and (167), the symbol c refers to the description with hexagonal axes'; i.e. the glide vector is , along [001]. In the description with rhombohedral axes', this glide vector is , along [111], i.e. the symbol of the glide plane would be n: cf. Table 1.5.4.4 .
Glide planes `e' occur in orthorhombic A-, C- and F-centred space groups, tetragonal I-centred and cubic F- and I-centred space groups. The geometric element of an e-glide plane is a plane shared by glide reflections with perpendicular glide vectors, with at least one glide vector along a crystal axis [cf. Section 1.2.3 and de Wolff et al. (1992)].
§Glide planes d occur only in orthorhombic F space groups, in tetragonal I space groups, and in cubic I and F space groups. They always occur in pairs with alternating glide vectors, for instance and . The second power of a glide reflection d is a centring vector.
Only the symbol m is used in the Hermann–Mauguin symbols, for both point groups and space groups.
††The inversion point is a centre of symmetry if n is odd.