Unit cells can be used to create new tilings. Strictly speaking, a unit cell is a square with sides measuring one unit. However, for the purposes of tessellations, unit cells can either be a square, equilateral triangle, or regular hexagon. Notice that these are the polygons involved in regular tessellations which is not a coincidence. The technique of unit cells takes advantage of this property. Patterns are drawn inside unit cells so that when the unit cells are repeated in the manner of the regular tessellations, the patterns repeat to form a tessellation.
Not all unit squares produce a valid tiling, however.
For example, the following unit cell produces a pattern that is
not enitrely made of polygons. Look at the white areas. There
are actually no white shapes, because the white areas are continuous
in the vertical direction. Thus, this pattern does not fit the
definition of tiling. A true tiling would have distinct shapes
arranged in a repeating pattern.
The cause of the problem is that the points on the red polygons do not line up. In other words, the points on the left side of the square need to line up with the points on the right side of the square; and the points on the top side of the square need to line up with the points on the bottom side of the square.
First, one corner of a unit square is drawn. (Let us assume for
simplicity that the upper-left corner is drawn.) The corner is
then reflected across the vertical axis of the unit square. Next,
the resulting pattern is reflected across the horizontal axis
to complete the unit square. These reflections ensure that points
on opposites will line up.
Here are two examples of unit cell tilings created using the reflection