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.


Printer.svg The Exploration File:Wallpapersymmetry.pdf
  • Printed copy of the Wallpaper Symmetry Exploration.
Printer.svg The Flow Chart File:Wall-flow.pdf
  • Copy of the flowchart


Geometric patterns

For the following geometric wallpaper patterns

  1. Choose a point and mark the lattice of all translations of the point.
  2. Mark all centers of rotation symmetry.
  3. Identify and mark mirror lines.
  4. 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. Heesch-TCTCC.svg
E. File:Heesch-TCCTGG.svg F. Heesch-CC6C6.svg

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).

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

Instructor:Wallpaper Symmetry Solutions (Instructors only)