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

International Tables for Crystallography (2013). Vol. D, ch. 3.4, p. 496


V. Janoveca* and J. Přívratskáb

aInstitute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-18221 Prague 8, 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:

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

Standard: symbols used in Section 3.1.3[link] , in the present chapter and in the software; suffixes (in italic) refer to the Cartesian crystallophysical coordinate system. BC: Bradley & Cracknell (1972[link]). AH: Altmann & Herzig (1994[link]). IT A: IT A (2005[link]), 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 x}{\sf y}{\sf z})] in a crystallographic basis (see e.g. Bradley & Cracknell, 1972[link]).

StandardBCAHIT AJonesStandardBCAHIT AJones
1 or e E E [{\sf 1}] [{\sf x},{\sf y},{\sf z}] [\bar 1] or i I I [{\bar{\sf 1}}]   [{\sf 0},{\sf 0},{\sf 0}] [\bar{\sf x},\bar{\sf y},\bar{\sf z}]
[6_{ z}] [C_{6}^{+}] [C_{6}^{+}] [{\sf 6^{+}}]   [{\sf 0},{\sf 0},{\sf z}] [{\sf x}-{\sf y},{\sf x},{\sf z}] [{\bar 6}_{ z}] [S_{3}^{-}] [S_{3}^{-}] [{\bar{\sf 6}^{+}}]   [{\sf 0},{\sf 0},{\sf z}] [{\sf y}-{\sf x},\bar{\sf x},\bar{\sf z}]
[3_{ z}] [C_{3}^{+}] [C_{3}^{+}] [{\sf 3^{+}}]   [{\sf 0},{\sf 0},{\sf z}] [{\bar {\sf y}},{\sf x}-{\sf y},{\sf z}] [{\bar 3}_{ z}] [S_{6}^{-}] [S_{6}^{-}] [{\bar {\sf 3}^{+}}]   [{\sf 0},{\sf 0},{\sf z}] [{\sf y},{\sf y}-{\sf x},\bar{\sf z}]
[2_{ z}] [C_{2}] [C_{2}] [{\sf 2}]   [{\sf 0},{\sf 0},{\sf z}] [\bar{\sf x},\bar{\sf y},{\sf z}] [m_{ z}] [\sigma_{h}] [\sigma_{h}] [{\sf m}]   [{\sf x},{\sf y},{\sf 0}] [{\sf x},{\sf y},\bar{\sf z}]
[3_{ z}^{2}] [C_{3}^{-}] [C_{3}^{-}] [{\sf 3^{-}}]   [{\sf 0},{\sf 0},{\sf z}] [{\sf y}-{\sf x},\bar{\sf x},{\sf z}] [{\bar 3}_{ z}^{5}] [S_{6}^{+}] [S_{6}^{+}] [{\bar {\sf 3}^{-}}]   [{\sf 0},{\sf 0},{\sf z}] [{\sf x}-{\sf y},{\sf x},\bar{\sf z}]
[6_{ z}^{5}] [C_{6}^{-}] [C_{6}^{-}] [{\sf 6^{-}}]   [{\sf 0},{\sf 0},{\sf z}] [{\sf y},{\sf y}-{\sf x},{\sf z}] [{\bar 6}_{ z}^{5}] [S_{3}^{+}] [S_{3}^{+}] [\bar{\sf 6}^{-}]   [{\sf 0},{\sf 0},{\sf z}] [\bar{\sf y},{\sf x}-{\sf y},\bar{\sf z}]
[2_{ x}] [C_{21}{^\prime}{^\prime}] [C_{21}{^\prime}{^\prime}] [{\sf 2}]   [{\sf x},{\sf 0},{\sf 0}] [{\sf x}-{\sf y},\bar{\sf y},\bar{\sf z}] [m_{ x}] [\sigma_{v1}] [\sigma_{v1}] [{\sf m}]   [{\sf x},{\sf 2}{\sf x},{\sf z}] [{\sf y}-{\sf x},{\sf y},{\sf z}]
[2_{x^\prime}] [C_{22}{^\prime}{^\prime}] [C_{22}{^\prime}{^\prime}] [{\sf 2}]   [{\sf 0},{\sf y},{\sf 0}] [\bar{\sf x},{\sf y}-{\sf x},\bar{\sf z}] [m_{x^\prime}] [\sigma_{v2}] [\sigma_{v2}] [{\sf m}]   [{\sf 2}{\sf x},{\sf x},{\sf z}] [{\sf x},{\sf x}-{\sf y},{\sf z}]
[2_{x{^\prime}{^\prime}}] [C_{23}{^\prime}{^\prime}] [C_{23}{^\prime}{^\prime}] [{\sf 2}]   [{\sf x},{\sf x},{\sf 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},{\sf 2}{\sf x},{\sf 0}] [{\sf y}-{\sf x},{\sf y},\bar{\sf z}] [m_{y}] [\sigma_{d1}] [\sigma_{d1}] [{\sf m}]   [{\sf x},{\sf 0},{\sf z}] [{\sf x}-{\sf y},\bar{\sf y},{\sf z}]
[2_{y{^\prime}}] [C_{22}{^\prime}] [C_{22}{^\prime}] [{\sf 2}]   [{\sf 2}{\sf x},{\sf x},{\sf 0}] [{\sf x},{\sf x}-{\sf y},\bar{\sf z}] [m_{y{^\prime}}] [\sigma_{d2}] [\sigma_{d2}] [{\sf m}]   [{\sf 0},{\sf y},{\sf z}] [\bar{\sf x},{\sf y}-{\sf x},{\sf 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},{\sf x},{\sf z}] [{\sf y},{\sf x},{\sf z}]