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.


  • Printed copy of the images from this exploration.
Printer.svg The Flow Chart File:Wall-flow.pdf
  • Copy of the flowchart



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



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. Wall-symmetry-p4m-stars.svg B. Dvonn-detail.svg
C. Wall-symmetry-pmm-xs.svg D. Wall-symmetry-p4.svg
E. Wall-symmetry-pg-zigs.svg F. Heesch-CC6C6.svg

Symmetry Groups

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

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

Instructor:Wallpaper Symmetry Solutions (Instructors only)