## The Geometry behind Tessellation

A finished tessellation picture

- One might ask, how can I make a tessellation? It is rather simple! You tessellation must be based on a basic shape that
tessellate.__can__

- A parallelogram or a square is a good example of a basic shape to start a tessellation. Start with one square and that will be your primary "cell." In tessellation, the "cell" is the basic shape that a "tile" is based upon. The "cell" is the basic tessellating shape; it is the shape that will be repeating. The "tile" would be the shape the "cell" makes. The bird in the example below is the "tile".

- Look at the example to the right; each square has the same image in it. Every part that is needed to make the full picture of the bird is in the square just not necessarily where you would think it needs to go.

- All you have to do is repeat the tiles and you get the entire tessellation and the entire image of the bird over and over again.

So what shapes can tessellate?

- There
are three
shapes that can tessellate.__regular__shape means that all the sides are equal and internal angles are equal. The three shapes are: Equilateral Triangle, Square, and Hexagon.__Regular__

- These shapes can also be flipped and rotated without affecting the shape’s ability to tessellation. Flipping the shapes can make the picture more dynamic, interesting, and pleasing to look at.

- Parallelograms are good for tessellation as well. This includes the set of shapes known as diamonds or rhomboids. Parallelograms can be squashed, tall, thin, or think, it does not make a difference with a parallelogram and its ability to tessellate.
- Hexagons do not have to have equal sides to tessellate either. Regular pentagons will not tessellate are but there are 14 known 5 sided shapes that
tessellate. Marjorie Rice was a major influence in finding these 5 sided shapes.__can__