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)