12.1 Tessellating Shapes

A tessellation is a pattern of identical shapes. You can make your own tessellation by fitting copies of a shape together, without gaps or overlap. You say the shape tessellates, or a tessellating shape. Here are some examples of shapes that tessellate with themselves.

Here are some examples of shapes that do not shape with themselves. There are gaps between the shapes.

When you make a tessellation you can move the shape by translating, rotation or reflecting it. 

Many tessellations are made by repeating a shape and using half-turn rotations of the same shape.

For example, this triangle

and using half-turn rotations of the same triangle fit together exactly to make a tessellation like this:

In any tessellation, the sum of the angles at the point where the vertices of the shapes meet is 360 degree. Look closely at three of the tessellations above.