Construction of Tilings with Transitivity Properties on the Square Grid
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 gro...
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| Main Authors: | , |
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| Format: | text |
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Archīum Ateneo
2024
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| Online Access: | https://archium.ateneo.edu/mathematics-faculty-pubs/269 https://doi.org/10.1007/978-3-031-57793-2_10 |
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| Institution: | Ateneo De Manila University |
| Summary: | 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. |
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