## 5 June 2018

### Tessellations

A tessellation is a pattern of figures that completely pave a flat surface, leaving no gaps between them and without overlapping. There are regular, semi-regular and irregular tessellations.

The only regular polygons paving a flat surface are equilateral triangles, squares and regular hexagons.

If we tried to pave a flat surface with regular pentagons, we would not be able because they overlap.

This is because the division of the flat surface which has $360º$ by the internal angle of a regular pentagon which measures $108º$ is not an integer.

But there are irregular pentagons paving a flat surface. They have already discovered $15$ different types, with the latter type discovered in $2015$ by Jennifer McLoud-Mann, Casey Mann and David Von Derau (University of Washington Bothell).