Tessellation refers to the covering of a surface using one or more geometric shapes, called tiles, without any overlaps or gaps. When we look at regular polygons, the ability to tessellate largely depends on the angles of the shapes involved.
A regular pentagon has interior angles of 108 degrees. When we try to fit these angles together at a point, the sum of the angles surrounding that point must equal 360 degrees for a tessellation to occur. However, when you arrange three pentagons together, their angles add up to 324 degrees (108 x 3), which leaves a gap of 36 degrees. This gap means that regular pentagons cannot fill space completely without leaving empty spaces or overlaps.
In contrast, polygons like squares or hexagons can tessellate because their angles allow them to fit perfectly around a point. This is why regular pentagons, despite being beautiful shapes, do not tessellate.