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In this paper we prove the existence of quasiperiodic rhombic substitution tilings with 2n-fold rotational symmetry, for any n. The tilings are edge-to-edge and use $$\lfloor {\frac{n}{2}\rfloor }$$ ⌊ n 2 ⌋ rhombic prototiles with unit length sides. We explicitly describe the substitution rule for the edges of the rhombuses, and prove the existence of the corresponding tile substitutions...
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