- Tessellating regular polygons
What is a Tessellation?
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.
Tessellation: A tiling over a plane with one or more figures such that the figures fill the plane with no overlaps and no gaps.
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.
Example 1: Draw a tessellation of equilateral triangles.
Extending the pattern, we have:
Example 2: Does a regular pentagon tessellate?
Tessellations can also be much more complicated. Check out http://www.mathsisfun.com/geometry/tessellation.html to see other tessellations and play with the Tessellation Artist, which has a link at the bottom of the page.
- You were told that equilateral triangles, squares, and regular hexagons are the only regular polygons that tessellate. Tessellate a square. Add color to your design.
- What is an example of a tessellated square in real life?
- How many regular hexagons will fit around one point? (First, recall how many degrees are in a hexagon, and then figure out how many degrees are in each angle of a regular polygon. Then, use this number to see how many of them fit around a point.)
- Using the information from #2, 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.