Statistical Destribution on Symmetry Groups

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Group theory is successfully applied to analysis of crystal structure. The symmetry of a crystalline substance is represented by one of the 32 point groups In this note a stochastic model is introduced for the distribution of crystalline substances among the 32 point groups. Consider a point group x. and take possible symmetry operations.which can be added to the x. at random. Assume the number of operations is given by Poisson distribution. Add the operations to the x and we get a point group generated by the operations and the x. A simulation study is carried out by the model to compave the result with the data of the distribution of crystalline substances.