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Sub Rosa, A System of Quasiperiodic Rhombic Substitution Tilings with n-Fold Rotational Symmetry
Tekijät: Kari J, Rissanen M
Kustantaja: SPRINGER
Julkaisuvuosi: 2016
Journal: Discrete and Computational Geometry
Tietokannassa oleva lehden nimi: DISCRETE & COMPUTATIONAL GEOMETRY
Lehden akronyymi: DISCRETE COMPUT GEOM
Vuosikerta: 55
Numero: 4
Aloitussivu: 972
Lopetussivu: 996
Sivujen määrä: 25
ISSN: 0179-5376
eISSN: 1432-0444
DOI: https://doi.org/10.1007/s00454-016-9779-1
Tiivistelmä
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 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 by proving that the interior can be tiled consistently with the given edge substitutions.
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 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 by proving that the interior can be tiled consistently with the given edge substitutions.
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