InternationalSpace-group symmetryTables for Crystallography Volume A Edited by M. I. Aroyo © International Union of Crystallography 2015 |
International Tables for Crystallography (2015). Vol. A, ch. 1.4, p. 47
## Section 1.4.1.4.6.1. Tetragonal space groups with one symmetry direction H. Wondratschek
^{e} |

In the space groups of the crystal class 4, rotation or screw rotation axes run in direction [001]; in the space groups of crystal class these are rotoinversion axes ; and in crystal class 4/*m* both occur. The rotation 4 of the point group may be replaced by screw rotations 4_{1}, 4_{2} or 4_{3} in the space groups with a *P* lattice. If the lattice is *I*-centred, 4 and 4_{2} or 4_{1} and 4_{3} occur simultaneously, together with rotoinversions.

In the space groups of crystal class 4/*m* with a *P* lattice, the rotations 4 can be replaced by the screw rotations 4_{2} and the reflection *m* by the glide reflection *n* such that four space-group types with a *P* lattice exist: *P*4/*m*, , *P*4/*n* and . Two more are based on an *I* lattice: *I*4/*m* and . In all these six space groups the short HM symbols and full HM symbols are the same.