Using Reflections to Create Tessellations

To create a tessellation using only reflections, you must first start out with a regular polygon. Here we have used a hexagon.

Next, you must choose a line of reflection, and then reflect the entire figure about this line. (NOTE: you may choose to manipulate the sides of the figure)

Finally, you continue the reflections until the tessellation is complete.

Many tessellations use what is known as a GLIDE REFLECTION. A glide reflections is simply a translation and a reflection used together. First the segment is manipulated, as seen in red here.


Next, the segment is reflected about a line of symmetry and then translated to the opposite side.

Finally, use glide reflections to tessellate the plane.

Click HERE to see how Escher used reflections to create works of art.