Tetragonal, hexagonal and cylindrical systems

International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

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International Tables for Crystallography (2006). Vol. D. ch. 1.1, pp. 25-26

Section 1.1.4.10.4.5. Tetragonal, hexagonal and cylindrical systems

A. Authier^a ^*

^a Institut de Minéralogie et de la Physique des Milieux Condensés, Bâtiment 7, 140 rue de Lourmel, 75015 Paris, France
Correspondence e-mail: aauthier@wanadoo.fr

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(i) Groups 4, 6 and $[A_{\infty}]$ :

There are 4 independent components.
(ii) Groups 422, 622 and $[A_{\infty}\infty A_{2}]$ :

There is 1 independent component.
(iii) Groups , and $[A_{\infty }\infty M]$ :

There are 3 independent components.
(iv) Groups , and $[(A_{\infty }/M)C]$ : all the components are equal to zero.
(v) Group $[\bar{4}]$ :

There are 4 independent components.
(vi) Group $[\bar{6} = 3/m]$ : with the same conventions as for group 3. There are 2 independent components.
(vii) Group $[\bar{4}2m]$ – twofold axis parallel to $[Ox_{1}]$ :

There are 2 independent components.
(viii) Group $[\bar{4}2m]$ – mirror perpendicular to $[Ox_{1}]$ (twofold axis at $[45^{\circ}]$ ):

The number of independent components is of course the same.
(ix) Group $[\bar{6}2/m]$ : with the same conventions as for group 3. There is 1 independent component.
(x) Groups , and $[(A_{\infty }/M) \infty (A_{2}/M)C]$ : all the components are equal to zero.