Tessellation is the covering of a flat surface with shapes so there is no space between. This is used in tiling and mosaics, and is a very ancient science. There are many different approaches to tessellating and I will only present one here.
If we start off with a random shape and then try to join it up, we find that no matter how hard we try, there are spaces between.
So now we make up a new shape, made up of the old one PLUS the space between. And we find that this new shape does tessellate!
But we could also have made up a new shape like this. And this tessellates as well!
So we have made 4 shapes that tessellate with themselves. And, guess what, they also tessellate with each other!
Here’s a few tessellations I designed for using as pavers or tiles. In putting these together I have used an old piece of Mac software called Claris Draw - it’s ideal for this and imports directly into PowerPoint.
Two pavers - self tessellating or tessellating with each other Slide 1
Four pavers - Each can tessellate with itself or combine to produce a 4 shape tessellation Slide 2
Five sided paver - Tessellation achieved by progressive 180 degree rotations Slide 3
Two pavers - each Self- tessellating or combined to produce 3d tessellating effect Slide 4
Highly interlocked tessellation Five sided paver with tessellation achieved by progressive 180 degree rotations to produce an undulating effect Slide 5
Tessellation achieved by progressive 90 degree rotations Slide 6