A tessellation is a tiling over a plane with one or more figures such that the figures fill the plane with no overlaps and no gaps. You have probably seen tessellations before. Examples of a tessellation are: a tile floor, a brick or block wall, a checker or chess board, and a fabric pattern. The following pictures are also examples of tessellations.
Notice the hexagon (cubes, first tessellation) and the quadrilaterals fit together perfectly. If we keep adding more, they will entirely cover the plane with no gaps or overlaps.
What if you were given a hexagon and asked to tile it over a plane such that it would fill the plane with no overlaps and no gaps?
How many regular hexagons will fit around one point?
Does a regular octagon tessellate?
Draw a tessellation of equilateral triangles.
Extending the pattern, we have:
Does a regular pentagon tessellate?
How many squares will fit around one point?
- Tessellate a square. Add color to your design.
- What is an example of a tessellated square in real life?
- Tessellate a regular hexagon. Add color to your design.
- You can also tessellate two regular polygons together. Try tessellating a regular hexagon and an equilateral triangle. First, determine how many of each fit around a point and then repeat the pattern. Add color to your design.
- Does a regular dodecagon (12-sided shape) tessellate? Why of why not?
- Does a kite tessellate? Why or why not?
Do the following figures tessellate?
To see the Review answers, open this PDF file and look for section 12.7.