Construction of Tilings with Transitivity Properties on the Square Grid
Document Type
Conference Proceeding
Publication Date
1-1-2024
Abstract
Tilings have been a subject of interest in discrete geometry for their algebraic and geometric properties. Their applications extend to other areas such as crystallography and mathematical morphology. In this paper, we study a class of tilings called a,b,c tilings where their respective symmetry groups form a orbits of vertices, b orbits of edges and c orbits of tiles. A method is presented where a,b,c tilings are derived and enumerated from the square grid using groups of symmetries involving 4-fold rotations. Conditions on a, b and c are provided for (a,b,c) tilings that arise. Using these conditions, examples of (a,a-1,c) tilings are obtained.
Recommended Citation
Tomenes, M.D., De Las Peñas, M.L.A.N. (2024). Construction of Tilings with Transitivity Properties on the Square Grid. In: Brunetti, S., Frosini, A., Rinaldi, S. (eds) Discrete Geometry and Mathematical Morphology. DGMM 2024. Lecture Notes in Computer Science, vol 14605. Springer, Cham. https://doi.org/10.1007/978-3-031-57793-2_10
