The reason for this lies in the measurements of the interior angles of a regular polygon. For a regular polygon to tessellate the plane, each interior angle must be a divisor of 360° because then there won't be any gaps where the polygons meet at each vertex.

Can a regular decagon tessellate?

A regular decagon does not tessellate. A regular polygon is a two-dimensional shape with straight sides that all have equal length.

What makes a shape tessellate?

A tessellation is a pattern created with identical shapes which fit together with no gaps. Regular polygons tessellate if the interior angles can be added together to make 360°.