The Tiler takes a collection of shapes from the Shaper, and tries to find a way of arranging them using the 17 crystallographic groups to make a region that would tile the plane periodically. When doing this, it keeps track of symmetry information, and stores a list of translations that will be examined later to find successful periodic translation pairs. In the example illustrated below, the tiler took a regular triangle and a triangular kite, and used the symmetry rules of the group p6 to create the 18 sided region that tiles the plane periodically. The search used by the tiler is essentially similar to the search used by the shaper.
The following illustration shows a rendering of a tiler search where it finds the correct composite region that will tile the plane periodically.