# Wallpaper Symmetry Exploration

From EscherMath

**Objective:**
Learn to recognize the lattice in a wallpaper pattern. Learn to use the flow chart to identify wallpaper symmetry groups.

## Materials

- Printed copy of the Wallpaper Symmetry Exploration.

- Copy of the flowchart

## Exploration

### Lattice

1. Mark the lattice of translations on this geometric pattern:

### Symmetries

2. For the following geometric wallpaper patterns

- Mark all centers of rotation symmetry. Clearly indicate the order of rotation.
- Identify and mark mirror lines and glide reflections.

A. | B. File:Honeycomb.svg |

C. | D. |

E. | F. |

### Symmetry Groups

3. Identify the symmetry group of each figure in the previous part.

4. For each of these sketches from Escher's regular division drawings, use the flow chart to identify the symmetry group of each pattern (ignore colors).

- Sketch #10 (Fish)
- Sketch #13 (Dragonflies)
- Sketch #17 (Parrots)
- Sketch #30 (Fish and boats)
- Sketch #85 (Fish, bats, lizards)

**Handin:**
This page with the geometric patterns marked, and all symmetry groups identified.

Instructor:Wallpaper Symmetry Solutions (Instructors only)