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The finite group notation used is: Z n: cyclic group of order n, D n: dihedral group isomorphic to the symmetry group of an n–sided regular polygon, S n: symmetric group on n letters, and A n: alternating group on n letters. The character tables then follow for all 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 ...
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 rotation (determinant of M = −1). The geometric symmetries of crystals are described by space groups, which ...
All of the discrete point symmetries are subgroups of certain continuous symmetries. They can be classified as products of orthogonal groups O( n ) or special orthogonal groups SO( n ). O(1) is a single orthogonal reflection, dihedral symmetry order 2, Dih 1 .
Symmetry elements of formaldehyde. C 2 is a two-fold rotation axis. σ v and σ v ' are two non-equivalent reflection planes.. In chemistry, molecular symmetry describes the symmetry present in molecules and the classification of these molecules according to their symmetry.
For example, 4 1 /a means that the crystallographic axis in question contains both a 4 1 screw axis as well as a glide plane along a. In Schoenflies notation, the symbol of a space group is represented by the symbol of corresponding point group with additional superscript. The superscript doesn't give any additional information about symmetry ...
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