Tables for
Volume F
Crystallography of biological macromolecules
Edited by E. Arnold, D. M. Himmel and M. G. Rossmann

International Tables for Crystallography (2012). Vol. F, ch. 2.1, pp. 48-49   | 1 | 2 |


J. Drentha*

aLaboratory of Biophysical Chemistry, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
Correspondence e-mail:

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The 11 enantiomorphic point groups

The point groups are presented as two stereographic projections (see Fig.[link] On the right is a projection of the symmetry elements, and on the left a projection of the general faces. They are arranged according to the crystal system to which they belong: triclinic, monoclinic etc. Different point groups are separated by full horizontal rules. The monoclinic point groups are given in two settings: in the conventional setting with the twofold axis along b (unique axis b), and the other setting with unique axis c. The b axis is horizontal in the projection plane, and the c axis is normal to the plane. Three-, four- and sixfold axes are always set along the c axis, normal to the plane. A special case is the trigonal system; either hexagonal axes or rhombohedral axes can be chosen. In the hexagonal case, the threefold axis is along the c axis. The other two axes are chosen along or between the twofold axes, which include an angle of [120^{\circ}]. In the rhombohedral setting, the threefold axis is along the body diagonal of the unit cell, and the unit cell vectors a, b and c are the shortest non-coplanar lattice vectors symmetrically equivalent with respect to the threefold axis (Fig.[link]). Symbols: [Scheme scheme1] Adapted with permission from IT A (2005[link]), Table[link] .

TRICLINIC 1 [Scheme scheme2]
MONOCLINIC 2 [Scheme scheme3] [Scheme scheme4]
ORTHORHOMBIC 222 [Scheme scheme5]
TETRAGONAL 4 [Scheme scheme6]
TETRAGONAL 422 [Scheme scheme7]
TRIGONAL Hexagonal axes 3 [Scheme scheme8]
TRIGONAL Rhombohedral axes 3 [Scheme scheme9]
TRIGONAL Hexagonal axes 321 [Scheme scheme10]
TRIGONAL Hexagonal axes 312 [Scheme scheme11]
TRIGONAL Rhombohedral axes 32 [Scheme scheme12]
HEXAGONAL 6 [Scheme scheme13]
HEXAGONAL 622 [Scheme scheme14]
CUBIC 23 [Scheme scheme15]
CUBIC 432 [Scheme scheme16]