A hierarchy of classification methods for patterns*

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Abstract
In the spirit of Felix Klein's “Erlangen Program” a methodical approach is developed to three levels of classification of geometric objects. These three levels are successive refinements of the classification by the crystallographic (symmetry) groups. The approach provides a systematic framework for most kinds of previously classified objects, such as dot patterns (= lattice complexes), circle or ellipse patterns (= circle packings, ellipse packings), tilings (tessellations) with equivalent tiles (or edges, or vertices), and many others.

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