Table 3.4.2.6

Janovec, V.; Přívratská

doi:10.1107/97809553602060000645

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

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International Tables for Crystallography (2006). Vol. D. ch. 3.4, p. 461

Table 3.4.2.6

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 3.4.2.6 | top | pdf |
Symbols of symmetry operations of the point group [6/mmm]

Standard: symbols used in Section 3.1.3 , in the present chapter and in the software; suffixes (in italic) refer to the Cartesian crystallophysical coordinate system. BC: Bradley & Cracknell (1972). AH: Altmann & Herzig (1994). IT A: IT A (2005), coordinates (in Sans Serif) are expressed in a crystallographic hexagonal basis. Jones: Jones' faithful representation symbols express the action of a symmetry operation of a vector $[({\sf xyz})]$ in a crystallographic basis (see e.g. Bradley & Cracknell, 1972).

Standard	BC	AH	IT A	Jones	Standard	BC	AH	IT A	Jones
1 or e	E	E	$[{\sf 1}]$	$[{\sf x,y,z}]$	$[\bar 1]$ or i	I	I	$[{\bar{\sf 1}}]$ $[{\sf 0,0,0}]$	$[\bar{\sf x},\bar{\sf y},\bar{\sf z}]$
$[6_{ z}]$	$[C_{6}^{+}]$	$[C_{6}^{+}]$	$[{\sf 6^{+}}]$ $[{\sf 0,0,z}]$	$[{\sf x-y,x,z}]$	$[{\bar 6}_{ z}]$	$[S_{3}^{-}]$	$[S_{3}^{-}]$	$[{\bar{\sf 6}^{+}}]$ $[{\sf 0,0,z}]$	$[{\sf y-x},\bar{\sf x},\bar{\sf z}]$
$[3_{ z}]$	$[C_{3}^{+}]$	$[C_{3}^{+}]$	$[{\sf 3^{+}}]$ $[{\sf 0,0,z}]$	$[{\bar {\sf y}},{\sf x-y},{\sf z}]$	$[{\bar 3}_{ z}]$	$[S_{6}^{-}]$	$[S_{6}^{-}]$	$[{\bar {\sf 3}^{+}}]$ $[{\sf 0,0,z}]$	$[{\sf y,y-x,}\bar{\sf z}]$
$[2_{ z}]$	$[C_{2}]$	$[C_{2}]$	$[{\sf 2}]$ $[{\sf 0,0,z}]$	$[\bar{\sf x},\bar{\sf y},{\sf z}]$	$[m_{ z}]$	$[\sigma_{h}]$	$[\sigma_{h}]$	$[{\sf m}]$ $[{\sf x,y,0}]$	$[{\sf x},{\sf y},\bar{\sf z}]$
$[3_{ z}^{2}]$	$[C_{3}^{-}]$	$[C_{3}^{-}]$	$[{\sf 3^{-}}]$ $[{\sf 0,0,z}]$	$[{\sf y-x},\bar{\sf x},{\sf z}]$	$[{\bar 3}_{ z}^{5}]$	$[S_{6}^{+}]$	$[S_{6}^{+}]$	$[{\bar {\sf 3}^{-}}]$ $[{\sf 0,0,z}]$	$[{\sf x-y},{\sf x},\bar{\sf z}]$
$[6_{ z}^{5}]$	$[C_{6}^{-}]$	$[C_{6}^{-}]$	$[{\sf 6^{-}}]$ $[{\sf 0,0,z}]$	$[{\sf y,y-x,z}]$	$[{\bar 6}_{ z}^{5}]$	$[S_{3}^{+}]$	$[S_{3}^{+}]$	$[\bar{\sf 6}^{-}]$ $[{\sf 0,0,z}]$	$[\bar{\sf y},{\sf x-y},\bar{\sf z}]$
$[2_{ x}]$	$[C_{21}{^\prime}{^\prime}]$	$[C_{21}{^\prime}{^\prime}]$	$[{\sf 2}]$ $[{\sf x,0,0}]$	$[{\sf x-y},\bar{\sf y},\bar{\sf z}]$	$[m_{ x}]$	$[\sigma_{v1}]$	$[\sigma_{v1}]$	$[{\sf m}]$ $[{\sf x,2x,z}]$	$[{\sf y-x,y,z}]$
$[2_{x^\prime}]$	$[C_{22}{^\prime}{^\prime}]$	$[C_{22}{^\prime}{^\prime}]$	$[{\sf 2}]$ $[{\sf 0,y,0}]$	$[\bar{\sf x},{\sf y-x},\bar{\sf z}]$	$[m_{x^\prime}]$	$[\sigma_{v2}]$	$[\sigma_{v2}]$	$[{\sf m}]$ $[{\sf 2x,x,z}]$	$[{\sf x,x-y,z}]$
$[2_{x{^\prime}{^\prime}}]$	$[C_{23}{^\prime}{^\prime}]$	$[C_{23}{^\prime}{^\prime}]$	$[{\sf 2}]$ $[{\sf x,x,0}]$	$[{\sf y},{\sf x},\bar{\sf z}]$	$[m_{x{^\prime}{^\prime}}]$	$[\sigma_{v3}]$	$[\sigma_{v3}]$	$[{\sf m}]$ $[{\sf x},\bar{\sf x},{\sf z}]$	$[\bar{\sf y},\bar{\sf x},{\sf z}]$
$[2_{y}]$	$[C_{21}{^\prime}]$	$[C_{21}{^\prime}]$	$[{\sf 2}]$ $[{\sf x,2x,0}]$	$[{\sf y-x},{\sf y},\bar{\sf z}]$	$[m_{y}]$	$[\sigma_{d1}]$	$[\sigma_{d1}]$	$[{\sf m}]$ $[{\sf x,0,z}]$	$[{\sf x-y},\bar{\sf y},{\sf z}]$
$[2_{y{^\prime}}]$	$[C_{22}{^\prime}]$	$[C_{22}{^\prime}]$	$[{\sf 2}]$ $[{\sf 2x,x,0}]$	$[{\sf x,x-y},\bar{\sf z}]$	$[m_{y{^\prime}}]$	$[\sigma_{d2}]$	$[\sigma_{d2}]$	$[{\sf m}]$ $[{\sf 0,y,z}]$	$[\bar{\sf x},{\sf y-x,z}]$
$[2_{y{^\prime}{^\prime}}]$	$[C_{23}{^\prime}]$	$[C_{23}{^\prime}]$	$[{\sf 2}]$ $[{\sf x},\bar{\sf x},{\sf 0}]$	$[\bar{\sf y},\bar{\sf x},\bar{\sf z}]$	$[m_{y{^\prime}{^\prime}}]$	$[\sigma_{d3}]$	$[\sigma_{d3}]$	$[{\sf m}]$ $[{\sf x,x,z}]$	$[{\sf y,x,z}]$