International
Tables for Crystallography Volume A1 Symmetry relations between space groups Edited by Hans Wondratschek and Ulrich Müller © International Union of Crystallography 2011 |
International Tables for Crystallography (2011). Vol. A1, ch. 2.1, pp. 75-76
Section 2.1.2.5.3. Space groups with a rhombohedral lattice^{a}Institut für Kristallographie, Universität, D-76128 Karlsruhe, Germany, and ^{b}Departamento de Física de la Materia Condensada, Facultad de Ciencias, Universidad del País Vasco, Apartado 644, E-48080 Bilbao, Spain |
The seven trigonal space groups with a rhombohedral lattice are often called rhombohedral space groups. Their HM symbols begin with the lattice letter R and they are listed with both hexagonal axes and rhombohedral axes.
Rules
Remarks
Example 2.1.2.5.7
, No. 146. Maximal klassengleiche subgroups of index 2 and 3. Comparison of the data for the settings `hexagonal axes' and `rhombohedral axes'. The data for the general position and the generators are omitted.
The sequence of the blocks has priority over the classification by increasing index. Therefore, in the setting `hexagonal axes', the subgroups of index 3 precede the subgroup of index 2.
In the tables, the lattice relations are simpler for the setting `hexagonal axes'.
The complete general position is listed for the maximal k-subgroups of index 3 in the setting `hexagonal axes'; only the generator is listed for rhombohedral axes.