# Wallpaper Symmetry Exploration

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**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

### Geometric patterns

For the following geometric wallpaper patterns

- Choose a point and mark the lattice of all translations of the point.
- Mark all centers of rotation symmetry.
- Identify and mark mirror lines.
- Use the flowchart to identify the symmetry group of each pattern.

A. File:Stars-p4m.svg | B. File:Honeycomb.svg |

C. File:Xcurve-pmm.svg | D. |

E. File:Heesch-TCCTGG.svg | F. |

### Recognizable figures

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)