Substitution tilings with dense tile orientations and n-fold rotational symmetry

Frettlöh D, Say-awen ALD, De Las Penas MLAN (2017)
INDAGATIONES MATHEMATICAE-NEW SERIES 28(1: SI): 120-131.

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It is shown that there are primitive substitution filings with dense tile orientations invariant under n-fold rotation for n is an element of {2, 3, 4, 5, 6, 8). The proof for dense tile orientations uses a general result about irrationality of angles in certain parallelograms. (C) 2016 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
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Frettlöh D, Say-awen ALD, De Las Penas MLAN. Substitution tilings with dense tile orientations and n-fold rotational symmetry. INDAGATIONES MATHEMATICAE-NEW SERIES. 2017;28(1: SI):120-131.
Frettlöh, D., Say-awen, A. L. D., & De Las Penas, M. L. A. N. (2017). Substitution tilings with dense tile orientations and n-fold rotational symmetry. INDAGATIONES MATHEMATICAE-NEW SERIES, 28(1: SI), 120-131. doi:10.1016/j.indag.2016.11.009
Frettlöh, D., Say-awen, A. L. D., and De Las Penas, M. L. A. N. (2017). Substitution tilings with dense tile orientations and n-fold rotational symmetry. INDAGATIONES MATHEMATICAE-NEW SERIES 28, 120-131.
Frettlöh, D., Say-awen, A.L.D., & De Las Penas, M.L.A.N., 2017. Substitution tilings with dense tile orientations and n-fold rotational symmetry. INDAGATIONES MATHEMATICAE-NEW SERIES, 28(1: SI), p 120-131.
D. Frettlöh, A.L.D. Say-awen, and M.L.A.N. De Las Penas, “Substitution tilings with dense tile orientations and n-fold rotational symmetry”, INDAGATIONES MATHEMATICAE-NEW SERIES, vol. 28, 2017, pp. 120-131.
Frettlöh, D., Say-awen, A.L.D., De Las Penas, M.L.A.N.: Substitution tilings with dense tile orientations and n-fold rotational symmetry. INDAGATIONES MATHEMATICAE-NEW SERIES. 28, 120-131 (2017).
Frettlöh, Dirk, Say-awen, A. L. D., and De Las Penas, M. L. A. N. “Substitution tilings with dense tile orientations and n-fold rotational symmetry”. INDAGATIONES MATHEMATICAE-NEW SERIES 28.1: SI (2017): 120-131.
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