My Most Unforgettable Characters: Representations of the Thirty-Two Crystallographic Point Groups
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The elements of symmetry or covering operations of a particular point group under a defined multiplication define a group. I have chosen to define these thirty-two basic point groups and to find all of the irreducible representations of each as an illustration of practical application of representation theory. The first section will deal with the basic theory of matrix representations of finite groups, the second with the covering operations and descriptions of the thirty-two point groups, and the third with the development of the matrix representations of these groups.