Table 3.4.2.5

Janovec, V.; Přívratská

doi:10.1107/97809553602060000645

International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

pdf | chapter contents | chapter index | related articles

International Tables for Crystallography (2006). Vol. D. ch. 3.4, p. 460

Table 3.4.2.5

V. Janovec^a ^* and J. Přívratská^b

^a Department of Physics, Technical University of Liberec, Hálkova 6, 461 17 Liberec 1, Czech Republic, and ^bDepartment of Mathematics and Didactics of Mathematics, Technical University of Liberec, Hálkova 6, 461 17 Liberec 1, Czech Republic
Correspondence e-mail: janovec@fzu.cz

Table 3.4.2.5 | top | pdf |
Symbols of symmetry operations of the point group $[m\bar 3m ]$

Standard: symbols used in Section 3.1.3 , in the present chapter and in the software; all symbols refer to the cubic crystallographic (Cartesian) basis, $[p\equiv[111]]$ (all $[{\underline{p}}]$ ositive), $[q\equiv[\bar1\bar11], \ r\equiv [1\bar1\bar1], \ s\equiv [\bar11\bar1] ]$ . BC: Bradley & Cracknell (1972). AH: Altmann & Herzig (1994). IT A: IT A (2005). Jones: Jones' faithful representation symbols express the action of a symmetry operation on a vector [(xyz)] (see e.g. Bradley & Cracknell, 1972).

Standard	BC	AH	IT A	Jones	Standard	BC	AH	IT A	Jones
1 or e	E	E	1		$[\bar{1}]$ or i	I	i	$[{\bar 1}]$	$[\bar{x},\bar{y},\bar{z}]$
$[2_{z}]$	$[C_{2z}]$	$[C_{2z}]$	2	$[{\bar x},{\bar y},z]$	$[m_{z}]$	$[\sigma_{z}]$	$[\sigma_{z}]$	m	$[x,y,{\bar z}]$
$[2_{x}]$	$[C_{2x}]$	$[C_{2x}]$	2	$[x,{\bar {y},{\bar z}}]$	$[m_{x}]$	$[\sigma_{x}]$	$[\sigma_{x}]$	m	$[{\bar x},y,z]$
$[2_{y}]$	$[C_{2y}]$	$[C_{2y}]$	2	$[{\bar x},y,{\bar z}]$	$[m_{y}]$	$[\sigma_{y}]$	$[\sigma_{y}]$	m	$[x,{\bar y},z]$
$[2_{xy}]$	$[C_{2a}]$	$[C_{2a}^{\prime}]$	2	$[y,x,{\bar z}]$	$[m_{xy}]$	$[\sigma_{da}]$	$[\sigma_{d1}]$	m $[x,{\bar x},z ]$	$[{\bar y},{\bar x},z]$
$[2_{x{\bar y}}]$	$[C_{2b}]$	$[C_{2b}^{\prime}]$	2 $[x,{\bar x},0 ]$	$[{\bar y},{\bar x},{\bar z}]$	$[m_{x{\bar y}}]$	$[\sigma_{db}]$	$[\sigma_{d2}]$	m
$[2_{zx}]$	$[C_{2c}]$	$[C_{2c}^{\prime}]$	2	$[z,{\bar y},x]$	$[m_{zx}]$	$[\sigma_{dc}]$	$[\sigma_{d3}]$	m $[{\bar x},y,x, ]$	$[{\bar z},y,{\bar x}]$
$[2_{z{\bar x}}]$	$[C_{2e}]$	$[C_{2e}^{\prime}]$	2 $[{\bar x},0,x ]$	$[{\bar z},{\bar y},{\bar x}]$	$[m_{z{\bar x}}]$	$[\sigma_{de}]$	$[\sigma_{d5}]$	m
$[2_{yz}]$	$[C_{2d}]$	$[C_{2d}^{\prime}]$	2	$[{\bar x},z,y]$	$[m_{yz}]$	$[\sigma_{dd}]$	$[\sigma_{d4}]$	m $[x,y,{\bar y} ]$	$[x,{\bar z},{\bar y}]$
$[2_{y{\bar z}}]$	$[C_{2f}]$	$[C_{2f}^{\prime}]$	$[0,y,{\bar y} ]$	$[{\bar x},{\bar z},{\bar y}]$	$[m_{y{\bar z}}]$	$[\sigma_{df}]$	$[\sigma_{d6}]$	m
$[3_{p}]$	$[C_{31}^{+}]$	$[C_{31}^{+}]$	$[3^{+}]$		$[{\bar 3}_{p}]$	$[S_{61}^{-}]$	$[S_{61}^{-}]$	$[{\bar 3}^{+}]$	$[{\bar z},{\bar x},{\bar y}]$
$[3_{q}]$	$[C_{32}^{+}]$	$[C_{32}^{+}]$	$[3^{+}]$ $[{\bar x},{\bar x},x]$	$[{\bar z},x,{\bar y}]$	$[{\bar 3}_{q}]$	$[S_{62}^{-}]$	$[S_{62}^{-}]$	$[{\bar 3}^{+}]$ $[{\bar x},{\bar x},x]$	$[z,{\bar x},y]$
$[3_{r}]$	$[C_{33}^{+}]$	$[C_{33}^{+}]$	$[3^{+}]$ $[x,{\bar x},{\bar x}]$	$[{\bar z},{\bar x},y]$	$[{\bar 3}_{r}]$	$[S_{63}^{-}]$	$[S_{63}^{-}]$	$[{\bar 3}^{+}]$ $[x,{\bar x},{\bar x}]$	$[z,x,{\bar y}]$
$[3_{s}]$	$[C_{34}^{+}]$	$[C_{34}^{+}]$	$[3^{+}]$ $[{\bar x},x,{\bar x}]$	$[z,{\bar x},{\bar y}]$	$[{\bar 3}_{s}]$	$[S_{64}^{-}]$	$[S_{64}^{-}]$	$[{\bar 3}^{+}]$ $[{\bar x},x,{\bar x}]$	$[{\bar z},x,y]$
$[3_{p}^{2}]$	$[C_{31}^{-}]$	$[C_{31}^{-}]$	$[3^{-}]$		$[{\bar 3}_{p}^{5}]$	$[S_{61}^{+}]$	$[S_{61}^{+}]$	$[{\bar 3}^{-}]$	$[{\bar y},{\bar z},{\bar x}]$
$[3_{q}^{2}]$	$[C_{32}^{-}]$	$[C_{32}^{-}]$	$[3^{-}]$ $[{\bar x},{\bar x},x]$	$[y,{\bar z},{\bar x}]$	$[{\bar 3}_{q}^{5}]$	$[S_{62}^{+}]$	$[S_{62}^{+}]$	$[{\bar 3}^{-}]$ $[{\bar x},{\bar x},x]$	$[{\bar y},z,x]$
$[3_{r}^{2}]$	$[C_{33}^{-}]$	$[C_{33}^{-}]$	$[3^{-}]$ $[x,{\bar x},{\bar x}]$	$[{\bar y},z,{\bar x}]$	$[{\bar 3}_{r}^{5}]$	$[S_{63}^{+}]$	$[S_{63}^{+}]$	$[{\bar 3}^{-}]$ $[x,{\bar x},{\bar x}]$	$[y,{\bar z},x]$
$[3_{s}^{2}]$	$[C_{34}^{-}]$	$[C_{34}^{-}]$	$[3^{-}]$ $[{\bar x},x,{\bar x}]$	$[{\bar y},{\bar z},x]$	$[{\bar 3}_{s}^{5}]$	$[S_{64}^{+}]$	$[S_{64}^{+}]$	$[{\bar 3}^{-}]$ $[{\bar x},x,{\bar x}]$	$[y,z,{\bar x}]$
$[4_{z}]$	$[C_{4z}^{+}]$	$[C_{4z}^{+}]$	$[4^{+}]$	$[{\bar y},x,z]$	$[{\bar 4}_{z}]$	$[S_{4z}^{-}]$	$[S_{4z}^{-}]$	$[{\bar 4}^{+}]$	$[y,{\bar x},{\bar z}]$
$[4_{x}]$	$[C_{4x}^{+}]$	$[C_{4x}^{+}]$	$[4^{+}]$	$[x,{\bar z},y]$	$[{\bar 4}_{x}]$	$[S_{4x}^{-}]$	$[S_{4x}^{-}]$	$[{\bar 4}^{+}]$	$[{\bar x},z,{\bar y}]$
$[4_{y}]$	$[C_{4y}^{+}]$	$[C_{4y}^{+}]$	$[4^{+}]$	$[z,y,{\bar x}]$	$[{\bar 4}_{y}]$	$[S_{4y}^{-}]$	$[S_{4y}^{-}]$	$[{\bar 4}^{+}]$	$[{\bar z},{\bar y},x]$
$[4_{z}^{3}]$	$[C_{4z}^{-}]$	$[C_{4z}^{-}]$	$[4^{-}]$	$[y,{\bar x},z]$	$[{\bar 4}_{z}^{3}]$	$[S_{4z}^{+}]$	$[S_{4z}^{+}]$	$[{\bar 4}^{-}]$	$[{\bar y},x,{\bar z}]$
$[4_{x}^{3}]$	$[C_{4x}^{-}]$	$[C_{4x}^{-}]$	$[4^{-}]$	$[x,z,{\bar y}]$	$[{\bar 4}_{x}^{3}]$	$[S_{4x}^{+}]$	$[S_{4x}^{+}]$	$[{\bar 4}^{-}]$	$[{\bar x},{\bar z},y]$
$[4_{y}^{3}]$	$[C_{4y}^{-}]$	$[C_{4y}^{-}]$	$[4^{-}]$	$[{\bar z},y,x]$	$[{\bar 4}_{y}^{3}]$	$[S_{4y}^{+}]$	$[S_{4y}^{+}]$	$[{\bar 4}^{-}]$	$[z,{\bar y},{\bar x}]$