A tessellation is a geometric pattern that can be repeated infinitely many times. The following one I created using GeoGebra. Creating this tessellation was my first attempt at using GeoGebra, so it took me a while to figure out a good way to create it. In order to see a more clear picture of the tessellation you can click on the picture.

I started just by creating a regular hexagon and went from there by adding different regular polygons along each edge. In creating this tesselation I liked the idea of having polygons that were “whole” and ones that were “divided.” This idea was used in the creation of the green rhombuses and blue triangles. Also, with the addition of the pink hexagons and purple trapezoids. I also really liked the look of the purple trapezoids almost enclosing some of the green rhombuses. The tessellation has lines of vertical lines symmetry through the two opposite points of the pink hexagons and the line that is shared by two adjacent purple trapezoids. There is also horizontal lines of symmetry through the middle of the pink hexagons/purple trapezoids, and the rows where it alternates between green rhombuses and blue triangles.

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Pretty design. To make an exemplar, you’d want to talk about how you made it, what you were going for, what you learned from making in it or the properties the tessellation has and why.