Here is an interactivity that allows you to create rotation patterns.

Move the blue dots to create a shape and use the slider to choose an angle of rotation.

Once you've explored the interactivity, take a look at the patterns below and see if you can recreate them. If you like, you can print out the patterns.

To make this picture, Charlie drew a kite and then told the robot to rotate it through an angle of $144^{\circ}$.

Alison used an angle of $216^{\circ}$ and got exactly the same pattern!

What other angles could they have used?

Can the other patterns be made using more than one angle?