International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by M. I. Aroyo

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. Wondratscheke

1.4.1.4.6.1. Tetragonal space groups with one symmetry direction

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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 [\overline{4}] these are rotoinversion axes [\overline{4}]; and in crystal class 4/m both occur. The rotation 4 of the point group may be replaced by screw rotations 41, 42 or 43 in the space groups with a P lattice. If the lattice is I-centred, 4 and 42 or 41 and 43 occur simultaneously, together with [\overline{4}] rotoinversions.

In the space groups of crystal class 4/m with a P lattice, the rotations 4 can be replaced by the screw rotations 42 and the reflection m by the glide reflection n such that four space-group types with a P lattice exist: P4/m, [P4_2/m], P4/n and [P4_2/n]. Two more are based on an I lattice: I4/m and [I4_1/a]. In all these six space groups the short HM symbols and full HM symbols are the same.








































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