Tessellations

Students were posed the following inquiry:

Regular tessellations (1) use identical regular polygons (2) to fill a space. The vertices (corners) of each polygon must match up with the vertices of other polygons.

You can produce exactly three regular tessellations:

Can you convince yourself that there are no more?


Test your ideas on this website: http://nrich.maths.org/content/id/4832/polygons.swf  


NOTE:

1. A tessellation is a pattern made of identical shapes:
   • the shapes must fit together without any gaps
   • the shapes should not overlap
2. Polygons are (2D) shapes with straight sides. To be a regular polygon all the sides and angles must be the same, eg. square, hexagon, pentagon.

Here are the students hard at work: