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

Abstract : 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.
Keywords : Rhombs Tiling Algorithm
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Gregory R. Maloney. On substitution tilings of the plane with n-fold rotational symmetry. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 17 no. 1 (1), pp.397-—414. ⟨10.46298/dmtcs.2108⟩. ⟨hal-01196852⟩



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