Discrete Mathematics & Theoretical Computer Science, Vol 17, No 1 (2015)

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On substitution tilings of the plane with n-fold rotational symmetry

Gregory Ross Maloney


A method is described for constructing, with computer assistance, planar substitution tilings that have n-fold rotational symmetry. This method uses as prototiles the set of rhombs with angles that are integer multiples of pi/n, and includes various special cases that have already been constructed by hand for low values of n. An example constructed by this method for n = 11 is exhibited; this is the first substitution tiling with elevenfold symmetry appearing in the literature.

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