Wallpaper Symmetry Exploration

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Time-45.svg

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

Materials

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

Exploration

Lattice

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

Heesch-TCTCC.svg

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. Wall-symmetry-p4m-stars.svg B. File:Honeycomb.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.

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).

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

Instructor:Wallpaper Symmetry Solutions (Instructors only)