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

International Tables for Crystallography (2013). Vol. D, ch. 3.4, p. 495


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:

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Symbols of symmetry operations of the point group [m\bar 3m ]

Standard: symbols used in Section 3.1.3[link] , 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[link]). AH: Altmann & Herzig (1994[link]). IT A: IT A (2005[link]). Jones: Jones' faithful representation symbols express the action of a symmetry operation on a vector [(xyz)] (see e.g. Bradley & Cracknell, 1972[link]).

StandardBCAHIT AJonesStandardBCAHIT AJones
1 or e E E 1 [x,y,z] [\bar{1}] or i I i [{\bar 1}]   [0,0,0] [\bar{x},\bar{y},\bar{z}]
[2_{z}] [C_{2z}] [C_{2z}] 2   [0,0,z] [{\bar x},{\bar y},z] [m_{z}] [\sigma_{z}] [\sigma_{z}] m   [x,y,0 ] [x,y,{\bar z}]
[2_{x}] [C_{2x}] [C_{2x}] 2   [x,0,0] [x,{\bar {y},{\bar z}}] [m_{x}] [\sigma_{x}] [\sigma_{x}] m   [0,y,z ] [{\bar x},y,z]
[2_{y}] [C_{2y}] [C_{2y}] 2   [0,y,0] [{\bar x},y,{\bar z}] [m_{y}] [\sigma_{y}] [\sigma_{y}] m   [x,0,z ] [x,{\bar y},z]
[2_{xy}] [C_{2a}] [C_{2a}^{\prime}] 2   [x,x,0] [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   [x,x,z ] [y,x,z]
[2_{zx}] [C_{2c}] [C_{2c}^{\prime}] 2   [x,0,x,] [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   [x,y,x ] [z,y,x]
[2_{yz}] [C_{2d}] [C_{2d}^{\prime}] 2   [0,y,y] [{\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}] [2]   [0,y,{\bar y} ] [{\bar x},{\bar z},{\bar y}] [m_{y{\bar z}}] [\sigma_{df}] [\sigma_{d6}] m   [x,y,y ] [x,z,y]
[3_{p}] [C_{31}^{+}] [C_{31}^{+}] [3^{+}]   [x,x,x] [z,x,y] [{\bar 3}_{p}] [S_{61}^{-}] [S_{61}^{-}] [{\bar 3}^{+}]   [x,x,x] [{\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^{-}]   [x,x,x] [y,z,x] [{\bar 3}_{p}^{5}] [S_{61}^{+}] [S_{61}^{+}] [{\bar 3}^{-}]   [x,x,x] [{\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^{+}]   [0,0,z] [{\bar y},x,z] [{\bar 4}_{z}] [S_{4z}^{-}] [S_{4z}^{-}] [{\bar 4}^{+}]   [0,0,z] [y,{\bar x},{\bar z}]
[4_{x}] [C_{4x}^{+}] [C_{4x}^{+}] [4^{+}]   [x,0,0] [x,{\bar z},y] [{\bar 4}_{x}] [S_{4x}^{-}] [S_{4x}^{-}] [{\bar 4}^{+}]   [x,0,0] [{\bar x},z,{\bar y}]
[4_{y}] [C_{4y}^{+}] [C_{4y}^{+}] [4^{+}]   [0,y,0] [z,y,{\bar x}] [{\bar 4}_{y}] [S_{4y}^{-}] [S_{4y}^{-}] [{\bar 4}^{+}]   [0,y,0] [{\bar z},{\bar y},x]
[4_{z}^{3}] [C_{4z}^{-}] [C_{4z}^{-}] [4^{-}]   [0,0,z] [y,{\bar x},z] [{\bar 4}_{z}^{3}] [S_{4z}^{+}] [S_{4z}^{+}] [{\bar 4}^{-}]   [0,0,z] [{\bar y},x,{\bar z}]
[4_{x}^{3}] [C_{4x}^{-}] [C_{4x}^{-}] [4^{-}]   [x,0,0] [x,z,{\bar y}] [{\bar 4}_{x}^{3}] [S_{4x}^{+}] [S_{4x}^{+}] [{\bar 4}^{-}]   [x,0,0] [{\bar x},{\bar z},y]
[4_{y}^{3}] [C_{4y}^{-}] [C_{4y}^{-}] [4^{-}]   [0,y,0] [{\bar z},y,x] [{\bar 4}_{y}^{3}] [S_{4y}^{+}] [S_{4y}^{+}] [{\bar 4}^{-}]   [0,y,0] [z,{\bar y},{\bar x}]