Tables for
Volume E
Subperiodic groups
Edited by V. Kopský and D. B. Litvin

International Tables for Crystallography (2006). Vol. E, ch. 1.2, pp. 13-14   | 1 | 2 |

Section 1.2.7. Origin

V. Kopskýa and D. B. Litvinb*

aDepartment of Physics, University of the South Pacific, Suva, Fiji, and Institute of Physics, The Academy of Sciences of the Czech Republic, Na Slovance 2, PO Box 24, 180 40 Prague 8, Czech Republic, and bDepartment of Physics, Penn State Berks Campus, The Pennsylvania State University, PO Box 7009, Reading, PA 19610-6009, USA
Correspondence e-mail:

1.2.7. Origin

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The origin has been chosen according to the following conventions:

  • (i) If the subperiodic group is centrosymmetric, then the inversion centre is chosen as the origin. For the three layer groups p4/n (L52), p4/nbm (L62) and p4/nmm (L64), we give descriptions for two origins, at the inversion centre and at ([-{1 \over 4}, -{1 \over 4}, 0]) from the inversion centre. This latter origin is at a position of high site symmetry and is consistent with having the origin on the fourfold axis, as is the case for all other tetragonal layer groups. The group symbols for the description with the origin at the inversion centre, e.g. [p4/n\, (\,{1 \over 4},{1 \over 4},0)], are followed by the shift [(\,{1 \over 4},{1 \over 4},0)] of the position of the origin used in the description having the origin on the fourfold axis.

  • (ii) For noncentrosymmetric subperiodic groups, the origin is at a point of highest site symmetry. If no symmetry is higher than 1, the origin is placed on a screw axis, a glide plane or at the intersection of several such symmetry elements.

Origin statement: In the line Origin immediately below the diagrams, the site symmetry of the origin is stated if different from the identity. A further symbol indicates all symmetry elements that pass through the origin. For the three layer groups p4/n (L52), p4/nbm (L62) and p4/nmm (L64) where the origin is on the fourfold axis, the statement `at [-{1 \over 4}, -{1 \over 4}, 0] from centre' is given to denote the position of the origin with respect to an inversion centre.

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