In my previous post, I showed you some adventurous ideas on how to tile floors. In this post, we examine other types of tilings.
In the first figure, the tiling is composed of squares and equilateral triangles.
In the second figure, the tiling is composed of hexagons (6-sided polygons) and equilateral triangles.
In the third figure, the tiling is made up of dodegacons (12-sided polygons), squares, and equilateral triangles.
The tilings above and in the previous post do not only display beautiful patterns. Mathematical considerations are needed to create such tilings. For instance, in the third figure, there are points where the vertices ofa a dodecahedron, a square, and two equilateral triangles meet. The interior angles of these polygons measure 150, 90, 120 degrees respectively. Observe that the angle measures add up to 360 degrees. Only combinations of polygons whose interior angles add up to 360 degrees will tile without gaps or overlaps (Can you see why?).