Symmetry and representation in a three dimensional space.

Schoenflies point groups are presented in terms of spatial partitions and Laue classes based on abstract groups. A much simpler system using only a minimal set of generators for three dimensional groups is then presented in the same form. This simplified treatment allows group operations of a given Laue class to be correlated to a greatly simplified Mulliken-style notation for irreducible representations of that class. Transformation matrix representations of point groups in the simplified style can then be manipulated according to their position in the class or to their sub-groups in very clear procedures. Simple rules can replace the large numbers of tables necessary in the Schoenflies approach. Some applications of the method are described. [ABSTRACT FROM AUTHOR]