Finite representation for seven crystal systems / Nurul Suhada Aziz - Aziz, Nurul Suhada (2012)
The developments of some rigid mathematical criteria of symmetry are required in order to make the idea of a molecular system as useful as possible. The first consideration was on the kinds of symmetry elements that a molecule may have and the symmetry operations generated by the symmetry elements presented in symmetry groups. The classification of finite symmetry groups in R3 has important applications in crystallography. Many chemical substances from crystals and their structures take the forms of crystalline lattices. This study present the classification of chemistry point groups according to the seven crystal systems. The generators can be described in terms of chemistry point groups' elements or abstract symmetry group elements accordingly. By using GAP, the possible relations between the set of generators and the finite representations for corresponding abstract groups of crystallographic point groups were determined. From the result of finite presentations of abstract symmetry groups, the generators and relations of chemistry point groups can be described using the symmetry elements of point groups.