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These groups are characterized by an n-fold improper rotation axis S n, where n is necessarily even. The S 2 group is the same as the C i group in the nonaxial groups section. S n groups with an odd value of n are identical to C nh groups of same n and are therefore not considered here (in particular, S 1 is identical to C s).
This is enantiomorphism, and the mirror images are said to be enantiomorphs of each other. The possibility of enantiomorphic crystals is determined by the crystal symmetry, i.e., by the point group of the crystal species. There are 32 possible point groups, and 22 of these are capable of forming enantiomorphs. [9]
In mathematics, a rod group is a three-dimensional line group whose point group is one of the axial crystallographic point groups. This constraint means that the point group must be the symmetry of some three-dimensional lattice. Table of the 75 rod groups, organized by crystal system or lattice type, and by their point groups:
In crystallography, a crystallographic point group is a three dimensional point group whose symmetry operations are compatible with a three dimensional crystallographic lattice. According to the crystallographic restriction it may only contain one-, two-, three-, four- and sixfold rotations or rotoinversions. This reduces the number of ...
The latter means, that enantiomorphic point groups describe chiral (enantiomorphic) structures. In the current table, "enantiomorphic" means that a group itself (considered as a geometric object) is enantiomorphic, like enantiomorphic pairs of three-dimensional space groups P3 1 and P3 2, P4 1 22 and P4 3 22. Starting from four-dimensional ...
In Hermann–Mauguin notation, space groups are named by a symbol combining the point group identifier with the uppercase letters describing the lattice type.Translations within the lattice in the form of screw axes and glide planes are also noted, giving a complete crystallographic space group.
Point groups are used to describe the symmetries of geometric figures and physical objects such as molecules. Each point group can be represented as sets of orthogonal matrices M that transform point x into point y according to y = Mx. Each element of a point group is either a rotation (determinant of M = 1), or it is a reflection or improper ...
The table below organizes the space groups of the monoclinic crystal system by crystal class. It lists the International Tables for Crystallography space group numbers, [ 2 ] followed by the crystal class name, its point group in Schoenflies notation , Hermann–Mauguin (international) notation , orbifold notation, and Coxeter notation, type ...