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

International Tables for Crystallography (2010). Vol. E, ch. 1.2, p. 16   | 1 | 2 |

Section 1.2.10. Generators

V. Kopskýa and D. B. Litvinb*

aFreelance research scientist, Bajkalská 1170/28, 100 00 Prague 10, Czech Republic, and bDepartment of Physics, The Eberly College of Science, Penn State – Berks Campus, The Pennsylvania State University, PO Box 7009, Reading, PA 19610–6009, USA
Correspondence e-mail:  u3c@psu.edu

1.2.10. Generators

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The line Generators selected states the symmetry operations and their sequence selected to generate all symmetrically equivalent points of the General position from a point with coordinates [x,y,z]. The identity operation given by (1) is always selected as the first generator. The generating translations are listed next, t(1, 0) for frieze groups, t(0, 0, 1) for rod groups, and t(1, 0, 0) and t(0, 1, 0) for layer groups. For centred layer groups, there is the additional centring translation t(1/2, 1/2, 0). The additional generators are given as numbers (p) which refer to the corresponding coordinate triplets of the general position and the corresponding entries under Symmetry operations; for centred layer groups, the first block `For (0, 0, 0)+ set' must be used.








































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