Tessellating the plane with convex polygons
In this article we give a panoramic view over the classification of tilings of the euclidean plane by using copies of a single convex polygon (convex monohedral tilings). First, we show that a tiling with regular poligons is only possible by using triangles, squares and regular hexagons, a fact well...
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| Formato: | Artículo revista |
| Lenguaje: | Español |
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Unión Matemática Argentina - Facultad de Matemática, Astronomía, Física y Computación
2022
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| Acceso en línea: | https://revistas.unc.edu.ar/index.php/REM/article/view/37469 |
| Aporte de: |
| Sumario: | In this article we give a panoramic view over the classification of tilings of the euclidean plane by using copies of a single convex polygon (convex monohedral tilings). First, we show that a tiling with regular poligons is only possible by using triangles, squares and regular hexagons, a fact well known by the ancient greeks, and that if the polygon is not convex then there are infinite possible tilings. In this way, we focus on convex tilings withnon-regular polygons. First, we show that any triangle or quadrilateral tiles the plane. Then, we show that a polygon that tiles the plane must have at most 6 edges. Next, we consider the case of hexagons and show that there are only 3 different families of convex hexagons tiling the plane. Finally, we deal with pentagons, whose classification is more involved, and could be completed recently in 2017. We will show that there are 15 different families of pentagons tiling the plane. |
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