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

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. E. ch. 1.2, p. 19

Table 1.2.14.2 

V. Kopskýa and D. B. Litvinb*

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 1.2.14.2 | top | pdf |
Projection of three-dimensional symmetry elements (layer and rod groups)

Symmetry element in three dimensions Symmetry element in projection
Arbitrary orientation
Symmetry centre [\bar{1}] Rotation point 2 at projection of centre
Parallel to projection direction
Rotation axis 2, 3, 4, 6 Rotation point 2, 3, 4, 6
Screw axis 21 Rotation point 2
31, 32 3
41, 42, 43 4
61, 62, 63, 64, 65 6
Rotoinversion axis [\bar{4}] Rotation point 4
[\bar{6}\equiv 3/m] 3 (with overlap of atoms)
[\bar{3}\equiv 3\times \bar{1}] 6
Reflection plane m Reflection line m
Glide plane with ⊥ component† Glide line g
Glide plane without ⊥ component† Reflection line m
Normal to projection direction
Rotation axis 2, 4, 6 Reflection line m
3 None
Screw axis 42, 62, 64 Reflection line m
21, 41, 43, 61, 63, 65 Glide line g
31, 32 None
Rotoinversion axis [\bar{4}] Reflection line m parallel to axis
[\bar{6}\equiv 3/m] Reflection line m perpendicular to axis
[\bar{3}\equiv 3 \times \bar{1}] Rotation point 2 (at projection of centre)
Reflection plane m None, but overlap of atoms
Glide plane with glide component t Translation t
† The term `with ⊥ component' refers to the component of the glide vector normal to the projection direction.