Table 1.1.2

Kopskyacute, V.; Litvin, D. B.

doi:10.1107/97809553602060000646

International
Tables for
Crystallography
Volume E
Subperiodic groups
Edited by V. Kopský and D. B. Litvin

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International Tables for Crystallography (2006). Vol. E. ch. 1.1, p. 2

Table 1.1.2

V. Kopský^a and D. B. Litvin^b ^*

^a Department of Physics, University of the South Pacific, Suva, Fiji, and Institute of Physics, The Academy of Sciences of the Czech Republic, Na Slovance 2, PO Box 24, 180 40 Prague 8, Czech Republic, and ^bDepartment of Physics, Penn State Berks Campus, The Pennsylvania State University, PO Box 7009, Reading, PA 19610-6009, USA
Correspondence e-mail: u3c@psu.edu

Table 1.1.2 | top | pdf |
Printed symbols for symmetry elements and for the corresponding symmetry operations

Printed symbol	Symmetry element and its orientation	Generating symmetry operation with glide or screw vector
m	Reflection plane, mirror plane (three dimensions)	Reflection through a plane
m	Reflection line, mirror line (two dimensions)	Reflection through a line
a, b or c	`Axial' glide plane	Glide reflection through a plane, with glide vector
a	⊥[010] or ⊥[001]	½a
b	⊥[100] or ⊥[001]	½b
c	⊥[100] or ⊥[010]	½c
	⊥[1 $[\bar{1}]$ 0] or ⊥[110]	½c
	⊥[100] or ⊥[010] or ⊥[ $[\bar{1}]$ $[\bar{1}]$ 0]	½c, hexagonal coordinate system
	⊥[1 $[\bar{1}]$ 0] or ⊥[120] or ⊥[ $[\bar{2}]$ $[\bar{1}]$ 0]	½c, hexagonal coordinate system
n	`Diagonal' glide plane (in noncentred cells only)	Glide reflection through a plane, with glide vector
n	⊥[001]	½(a + b)
e	`Double' glide plane ⊥[001] (in centred cells only)	Two glide reflections through planes with glide vectors ½a and ½b
g	Glide line (two dimensions)	Glide reflection through a line, with glide vector
g	⊥[01]; ⊥[10]	½a; ½b
1	None	Identity
2, 3, 4, 6	n-fold rotation axis, n (three dimensions)	Counterclockwise rotation of 360/n degrees about an axis
2, 3, 4, 6	n-fold rotation point, n (two dimensions)	Counterclockwise rotation of 360/n degrees about a point
$[\bar{1}]$	Centre of symmetry, inversion centre	Inversion through a point
$[\bar{2}]$ = m, $[\bar{3}]$ , $[\bar{4}]$ , $[\bar{6}]$	Rotoinversion axis, $[\bar{n}]$	Counterclockwise rotation of 360/n degrees around an axis, followed by inversion through a point on the axis
2₁, 3₁, 3₂, 4₁, 4₂, 4₃, 6₁, 6₂, 6₃, 6₄, 6₅	n-fold screw axes, n_p	Right-handed screw rotation of 360/n degrees around an axis, with screw vector (p/n)t; t is the shortest translation vector parallel to the axis in the direction of the screw