Tessellations

A tessellation is a repeated geometric design that covers a plane without any gaps or spaces.

Some shapes can be used to tessellate the plane, while other shapes cannot. For example, a square or an equilateral triangle can tessellate the plane (in fact any triangle or parallelogram can), but if you try to cover the plane with a regular pentagon, you'll find there's no way to do it without leaving gaps.

The same shape can be sometimes be used to tessellate the plane in more than one way. The figures below show three different tessellations using the same rhombus.

A tessellation can also use more than one shape, as shown below: