12.3 Tessellations using rotations

Repetitive tiling patterns spread across a plane to create amazing prints- this is what tessellations are. They are very colorful and eye catchy in so many level and you can see a lot of these prints everywhere, like in frames, flooring, wallpapers, graphics, icons and more.

Tessellation exhibits symmetry at its finest form. There are four kinds of symmetry in a plane, Translation, Reflection, Rotation and Glide Reflection. Most of the tessellations we see uses Translation symmetry where every regular polygon are placed side by side with each other, preventing gaps to be present in between them,

Reflection Symmetry on the other hand is flipping an image through the use of either the x axis or the y axis. Reflections can also be flipped through at a certain angle. Then there’s the Rotation symmetry where the images to be repeated are rotated at a certain angle and then placed side by side with each other, preventing any gaps to form in between. The last type is the Glide Reflection which combines the technique used in both translation symmetry and reflection symmetry. Each of these tessellation have their own axis of symmetry which is used to create all those distinct patterns that they have.

We will be learning more about tessellations in the introduction in 12.1, and then we will be looking at how to make one using translation and reflection symmetry in 12.2 and using rotation symmetry in 12.3. You can also try creating one on your own with the help of a tessellations creator online.

Tessellations using rotations

We have a square tile on the floor, and we rotate it around its center. When it is turned 90°, you can see the tile in its original place as if it has never moved at all. Then, we can conclude that the square tile has a rotational symmetry of 90°. In the previous section, we have learned that some shapes can reflect by flipping them over. The number of ways that a particular shape can reflect is dictated by the number of axes of reflection symmetry it has. We will learn how to find out that number of axes of symmetry in this section.


  • 1.
    Name a polygon that has a rotational symmetry of:
  • 2.
    Find the axe(s) of reflection symmetry for the polygons below.
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Tessellations using rotations

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