Point symmetry groups of all distorted configurations of a molecule form a lattice

1990 ◽  
Vol 4 (1) ◽  
pp. 377-381 ◽  
Author(s):  
Paul G. Mezey
Keyword(s):  
Point Symmetry ◽  
Symmetry Groups

Automated Symmetry Exploitation in Engineering Analysis

2004 ◽  
Author(s):  
Krishnan Suresh
Keyword(s):  
Irreducible Representations ◽  
Point Symmetry ◽  
Symmetry Groups ◽  
Engineering Analysis ◽  
Symmetry Detection ◽  
Important Concept ◽  
Improve Accuracy ◽  
Speed Up ◽  
Boundary Mapping ◽  
Cell Construction

It is well known that one can exploit symmetry to speed-up engineering analysis and improve accuracy, at the same time. Not surprisingly, most CAE systems have standard ‘provisions’ for exploiting symmetry. However, these provisions are inadequate in that they needlessly burden the design engineer with time consuming and error-prone tasks of symmetry detection, symmetry cell construction and reformulation. In this paper, we propose and discuss an automated methodology for symmetry exploitation. First, we briefly review the theory of point symmetry groups that symmetry exploitation rests on. We then address symmetry detection and ‘symmetry cell’ construction. We then address an important concept of boundary mapping of symmetry cells, and relate it to the irreducible representations of point symmetry groups. By formalizing these concepts, we show how automated symmetry exploitation can be achieved, and discuss an implementation of the proposed work within the FEMLAB CAE environment.

scholarly journals From teaching experience. VII. Subordination of symmetry groups and crystallographic criterion of harmony

2021 ◽  
Vol 2 ◽  
pp. 19-22
Author(s):  
Yu. L. Voytekhovsky ◽  
Keyword(s):  
Teaching Experience ◽  
Point Symmetry ◽  
Symmetry Groups ◽  
Outstanding Scientist ◽  
Saint Petersburg ◽  
University Course ◽  
The University

It is shown by the example of the fences of Saint Petersburg that they combine the borders of all seven symmetry groups in different ways. A criterion is proposed: a lattice is harmonious if the symmetry groups of the borders are subordinate, otherwise it is eclectic. According to the author’s experience, such an approach on the border of crystallography and architecture facilitates the perception of the topic on the subordination of 32 point symmetry groups in the university course of crystallography. The article is dedicated to the memory of the outstanding scientist and popularizer of mineralogy Professor A. G. Bulakh.

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