Background vocabulary

A tessellation is a plane (flat surface) of tiles with one or more geometric shapes (tiles) that fit together with no overlaps and no gaps or spaces between the tiles.

Example of how to create a tessellation

  • Start with a square:
  • Cut part of the left side of the square and slide it directly to the right side of the square.
  • Cut part of the bottom side of the square and slide it directly to the top side of the square.

Construction of a tessellation


Make your own










Tesselation extensions

  • What other shapes can you tessellate?
  • What different shapes can you combine to make a tessellation?
  • What are the properties of shapes that tesselate and do not tesselate?
  • Someone said. What is changes in one place must be made up for elsewhere. What do they mean?
    • Does this assume the starting shape must be able to be tesselated?
    • How do the areas of the shapes before the change and after the change compare?
    • They suggested to start with a shape, which can be tesselated, (square, equlateral triangle, equalateral hexagon, ...) cut away a part and move it along the perimeter to the remaining part of the shape. Repeat as desired and the new shape should be the same area and tesselate.
  • Draw a pattern on a square gird. Use the grid to cut and reshape the pattern as suggested above.



Dr. Robert Sweetland's notes
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