Answer
A tessellations is a type of art that is used to define a relationship between geometry and the visual arts. Tessellations are created by repeated use of same figures that will leave no gap and no overlaps and thus cover whole plane.
To create a tessellation the primary requirement is that the sum of the measures of the angles of a regular polygon that are together at each vertex must be \[360{}^\circ \]. To determine whether a tessellation can be created or not, use the formula \[\left( n-2 \right)\times 180{}^\circ \] that compute the sum of the measures of the angle of a regular hexagon and then divide it by the sides of a hexagon to find the measure of each angle.
Compute measure of each angle:
\[\begin{align}
& \text{measure of angle}=\frac{\left( n-2 \right)\times 180{}^\circ }{n} \\
& =\frac{\left( 6-2 \right)\times 180{}^\circ }{6} \\
& =\frac{4\times 180{}^\circ }{6} \\
& =120{}^\circ
\end{align}\]
The measure of each angle of a regular hexagon is \[120{}^\circ \]. Hence, the three regular hexagon fill in \[3\times 120{}^\circ =360{}^\circ \]and thus leaves no gap that fulfill the requirement of forming a tessellation, that is the measure of each angle at each vertex must be \[360{}^\circ \] by regular 6-sided polygons.
Hence, a tessellation can be created using only regular 6-sided polygon.
