# Making a Tessellation

Tessellation 1

Tessellation 2

To start making my tessellations, I began by making different shapes and seeing how they fit together in a nice way. My goal was to use curved lines in a tessellation because I think it gives them less of the standard pattern look. To make the tessellation I was going to make a design in one square grid and then reflect it multiple times. I wanted some of the shapes to connect and make new shapes when I reflected my original design. In my first tessellation, I used a lot of arc lines (semi circles) in corners of my original square and straight lines in the corners. I wasn’t really sure how it was going to look when I reflected it but in the end, hearts were the main new shape created by reflected my image. After getting a better feel of how an image might look after being reflected on Geogebra, I made a second tessellation. I really wanted to continue connecting the shapes so I again used arc lines in the corners this time which created a circle in the corner were 4 reflections met. After practice with the first tessellation, I feel that this one looks more complete.

Next, I researched what type of tessellation I had created. We had discussed in class that a regular tessellation was made up of congruent regular polygons. Also, we mentioned that a semi regular tessellation is made up of polygons so that every vertex is identical. Neither of these necessarily fit my images. I found that there are also demi regular tessellations as well. These tessellations can involve curved shapes not just polygons. However, I guess there is some debate in mathematics whether these are actually tessellations. I think both my images fit between a semi regular tessellation and a demi tessellation. This is because I did use some polygons but not all my vertexes are the same. I also used a bunch of curved lines, but not to the extent of the images I had seen when looking at demi regular tessellation.