5 June 2018


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).

The GIFs above were made by Adam Cole.

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