Unlike these hexafoils of ours, where whole shapes intertwine, in Gothic architecture the hexafoil was represented only as an outline of six overlapping circles.
The patterns are very simple and you can include them in your collection of geometric design elements, just to be ready until you get an idea on how to use them. Four patterns consist of hexafoils formed by overlapping circles, and the fifth consists of an elongated hexagon swirled around the center, whereby a star-centered hexafoil is obtained.