International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. B. ch. 1.4, p. 113

Table A1.4.2.5 

U. Shmueli,a* S. R. Hallb and R. W. Grosse-Kunstlevec

aSchool of Chemistry, Tel Aviv University, 69 978 Tel Aviv, Israel, bCrystallography Centre, University of Western Australia, Nedlands 6907, WA, Australia, and  cLawrence Berkeley National Laboratory, 1 Cyclotron Road, Mailstop 4-230, Berkeley, CA 94720, USA
Correspondence e-mail:  ushmueli@post.tau.ac.il

Table A1.4.2.5 | top | pdf |
Rotation matrices for face-diagonal axes

The symbols for face-diagonal twofold rotations are 2′ and 2′′. The face-diagonal axis direction is determined by the axis of the preceding rotation N x, N y or N z. Note that the single prime ′ is the default and may be omitted.

Preceding rotation Rotation Axis Matrix
N x 2′ b − c [\pmatrix{\bar{1}&0&0\cr0&0&\bar{1}\cr0&\bar{1}&0\cr}]
2′′ b + c [\pmatrix{\bar{1}&0&0\cr0&0&1\cr0&1&0\cr}]
N y 2′ a − c [\pmatrix{0&0&\bar{1}\cr0&\bar{1}&0\cr\bar{1}&0&0\cr}]
2′′ a + c [\pmatrix{0&0&1\cr0&\bar{1}&0\cr1&0&0\cr}]
N z 2′ a − b [\pmatrix{0&\bar{1}&0\cr\bar{1}&0&0\cr0&0&\bar{1}\cr}]
2′′ a + b [\pmatrix{0&1&0\cr1&0&0\cr0&0&\bar{1}\cr}]