Table 2.2.14.2

Hahn, Th.; Looijenga-Vos, A.

doi:10.1107/97809553602060000505

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

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International Tables for Crystallography (2006). Vol. A. ch. 2.2, p. 34

Table 2.2.14.2

Th. Hahn^a ^* and A. Looijenga-Vos^b ^‡

^a Institut für Kristallographie, Rheinisch-Westfälische Technische Hochschule, Aachen, Germany, and ^bLaboratorium voor Chemische Fysica, Rijksuniversiteit Groningen, The Netherlands
Correspondence e-mail: hahn@xtl.rwth-aachen.de

Table 2.2.14.2 | top | pdf |
Projections of crystallographic symmetry elements

Symmetry element in three dimensions	Symmetry element in projection
Arbitrary orientation
$[\left.\!\matrix{\hbox{Symmetry centre}\hfill &\bar{1}\hfill\cr \hbox{Rotoinversion axis} &\bar{3} \equiv 3 \times \bar{1}\hfill\cr}\right\}]$	Rotation point 2 (at projection of centre)
Parallel to projection direction
Rotation axis 2; 3; 4; 6	Rotation point 2; 3; 4; 6
$[\!\matrix{\hbox{Screw axis}\hfill& 2_{1}\hfill\cr & 3_{1},3_{2}\hfill\cr & 4_{1},4_{2},4_{3}\hfill\cr & 6_{1},6_{2},6_{3},6_{4},6_{5}\hfill\cr}]$	$[\!\matrix{\hbox{Rotation point}\hfill &2\hfill\cr & 3\hfill\cr & 4\hfill\cr & 6\hfill\cr}]$
$[\!\matrix{\hbox{Rotoinversion axis}\hfill &\bar{4}\hfill\cr & \bar{6} \equiv 3/m\hfill\cr\cr & \bar{3} \equiv 3 \times \bar{1}\hfill\cr}]$	$[\!\matrix{\hbox{Rotation point}\hfill &4\hfill\cr &3, \hbox{with overlap}\hfill\cr & \quad \hbox{of atoms}\hfill\cr &6\hfill\cr}]$
Reflection plane m	Reflection line m
Glide plane with $[\perp]$ component^†	Glide line g
Glide plane without $[\perp]$ component^†	Reflection line m
Normal to projection direction
$[\!\matrix{\hbox{Rotation axis}\hfill &2\semi\ 4\semi \ 6\hfill\cr & 3\hfill\cr}]$	$[\!\matrix{\hbox{Reflection line } m\hfill\cr \hbox{None}\hfill\cr}]$
$[\!\matrix{\hbox{Screw axis}\hfill & 4_{2}\semi\ 6_{2},6_{4}\hfill\cr & 2_{1}\semi\ 4_{1},4_{3}\semi\ 6_{1},6_{3},6_{5}\hfill\cr & 3_{1},3_{2}\hfill\cr}]$	$[\!\matrix{\hbox{Reflection line } m\hfill\cr \hbox{Glide line }g\hfill\cr \hbox{None}\hfill\cr}]$
$[\!\matrix{\hbox{Rotoinversion axis}\hfill &\bar{4}\hfill\cr & \bar{6} \equiv 3/m\hfill\cr\cr\cr &\bar{3} \equiv 3 \times \bar{1}\hfill}]$	$[\!\matrix{\hbox{Reflection line }m \hbox{ parallel to axis}\hfill\cr \hbox{Reflection line }m \hbox{ perpendicular}\hfill\cr\quad\hbox{to axis (through projection of}\hfill\cr\quad\hbox{inversion point)}\hfill\cr \hbox{Rotation point 2 (at projection}\hfill\cr\quad\hbox{of centre)}\hfill\cr}]$

Reflection plane m	None, but overlap of atoms
Glide plane with glide vector t	Translation with translation vector t

^†The term `with $[\perp]$ component' refers to the component of the glide vector normal to the projection direction.