Pattern Block Exploration

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Time-30.svg

Objective: Gain familiarity with regular polygon tessellations of the plane.

Materials needed: Pattern blocks. There are a number of "virtual pattern blocks" applets on the web. One of the best is here [1].

In this exploration, "touch" means to share an edge. Corner touches don’t count.

  1. Warm up by making the three regular tessellations.
  2. Make some tessellations using combinations of triangles and squares:
    1. Can you make one so that no square touches another square?
    2. Can you make one so that each square touches exactly one other square?
    3. Can you make one so that each square touches exactly two other squares?
    4. Can you make one so that each square touches exactly three other squares?
  3. Can you make a tessellation using only hexagons and squares?
  4. Make some tessellations using combinations of triangles, squares, and hexagons:
    1. Can you make one so that no shape touches another block of the same shape? (This also means no tiles of the same color touch.)
    2. Can you make one so that no square touches a hexagon?
  5. Make more tessellations using all the tiles.

Handin: A sheet with answers to all questions.