Abstract
For each n ∈ ℕ we construct a substitution rule using the set of rhombs with angles (πk)/n. These substitution rules generate a local isomorphism class of tilings closed under rotation of order 2n, and also admit singular tilings fixed under a rotation of order n. The scaling factors for this set of substitution rules includes algebraic numbers of every rank.
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Harriss, E. Non-Periodic Rhomb Substitution Tilings that Admit Order n Rotational Symmetry. Discrete Comput Geom 34, 523–536 (2005). https://doi.org/10.1007/s00454-005-1175-1
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DOI: https://doi.org/10.1007/s00454-005-1175-1