Sub Rosa, A System of Quasiperiodic Rhombic Substitution Tilings with n-Fold Rotational Symmetry



: Kari J, Rissanen M

Publisher: SPRINGER

: 2016

: Discrete and Computational Geometry

: DISCRETE & COMPUTATIONAL GEOMETRY

: DISCRETE COMPUT GEOM

: 55

: 4

: 972

: 996

: 25

: 0179-5376

: 1432-0444

DOI: https://doi.org/10.1007/s00454-016-9779-1


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.



Last updated on 2024-26-11 at 21:36