- Go to  and look at Hop’s 17 animated wallpaper groups (p1, p4, pgg, and p4m are especially good). For each one, there are links underneath that lead to animations. What are these animations demonstrating?
- Look at more examples of wallpaper patterns at .
- What rotation orders can appear as symmetries of a wallpaper pattern?
- Can a wallpaper pattern have an order 4 rotation symmetry as well as an order 3 rotation symmetry?
- Can a wallpaper pattern have an order 4 rotation symmetry as well as an order 6 rotation symmetry?
- Explain the difference between frieze patterns and wallpaper patterns.
- Make a wallpaper pattern using Escher Web Sketch. Print it out and mark all its symmetries. Which symmetry group does your pattern have?
- Try the modify cell button. What is the significance of the black "cell" in the applet? What is the significance of the red part of the cell?