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Each crystallographic point group defines the (geometric) crystal class of the crystal. The point group of a crystal determines, among other things, the directional variation of physical properties that arise from its structure, including optical properties such as birefringency , or electro-optical features such as the Pockels effect .
A reflection plane m within the point groups can be replaced by a glide plane, labeled as a, b, or c depending on which axis the glide is along. There is also the n glide, which is a glide along the half of a diagonal of a face, and the d glide, which is along a quarter of either a face or space diagonal of the unit cell.
For example, in its ground (N) electronic state the ethylene molecule C 2 H 4 has D 2h point group symmetry whereas in the excited (V) state it has D 2d symmetry. To treat these two states together it is necessary to allow torsion and to use the double group of the molecular symmetry group G 16 .
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). The S 8 table reflects the 2007 discovery of errors in older references. [4] Specifically, (R x, R y) transform not as ...
The isometric crystal system class names, point groups (in Schönflies notation, Hermann–Mauguin notation, orbifold, and Coxeter notation), type, examples, international tables for crystallography space group number, [2] and space groups are listed in the table below. There are a total 36 cubic space groups.
A crystal system is a set of point groups in which the point groups themselves and their corresponding space groups are assigned to a lattice system. Of the 32 crystallographic point groups that exist in three dimensions, most are assigned to only one lattice system, in which case both the crystal and lattice systems have the same name. However ...
The orthorhombic crystal system class names, examples, Schönflies notation, Hermann-Mauguin notation, point groups, International Tables for Crystallography space group number, [2] orbifold notation, type, and space groups are listed in the table below.
In geometry, a point group is a mathematical group of symmetry operations (isometries in a Euclidean space) that have a fixed point in common. The coordinate origin of the Euclidean space is conventionally taken to be a fixed point, and every point group in dimension d is then a subgroup of the orthogonal group O(d).