# Wallpaper Exploration

From EscherMath

**Objective:**
Discover basic information about wallpaper patterns

- Go to [1] 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 [2].
- 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?

**Handin:**
A sheet with answers to all questions.