Frieze Functions

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This Demonstration makes use of the following table of recipes to create frieze functions, represented by series of the form , with complex coefficients . Let represent a half-turn, and perpendicular mirror symmetries, and a glide reflection along the axis.


The functions used here are truncated to


according to the rules. For example, gives

and there would be four interior terms in the functions for and .

Only two copies of a unit cell are shown.


Contributed by: Izidor Hafner (February 2016)
Open content licensed under CC BY-NC-SA



The recipes are taken from [1, p. 59].


[1] F. A. Farris, Creating Symmetry, The Artful Mathematics of Wallpaper Patterns, Princeton: Princeton University Press, 2015.

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