AlgNet/GeoNet: A Union City School District Summer Enrichment Program
Using technology not simply to do things better, but to do better things.


A Tessellation or "Wallpaper" pattern extends infinitely in two dimensions, covering the plane without gaps or overlaps.

There are only seventeen distinct classes of wallpaper patterns. The basis for the classification is the presence and relative placement of mirrors, centers of rotations, translations, and glide reflections.

Given a guide that illustrates the seventeen wallpaper patterns, we will work in small groups to investigate these patterns.

  1. Examine a collection of tessellations created from pattern blocks. Identify the locations of mirrors, centers and vectors. Note that continuity of each pattern depends on the relative placement of these elements.
  2. A more difficult task is to create tessellations with the blocks that are an example of each of the seventeen types of wallpaper patterns. Why might some be more difficult than others to create?

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