This “swirly” tessellation was created a while back as an adaptation of Tomoko Fuse’s swirly square tessellation (seen here folded by Melisande) applied to a hexagon and triangle tessellation pattern
Begin with a regular hexagonal twist, but use pleats three creases wide – resist the urge to make a three crease wide hexagon, keep the little hexagon sitting on top – twist that little hexagon back in the direction opposite to the way the big pleats want to go, and then begin to collapse the whole thing into a sort of star shape. Notice in the second picture where the twisting begins to reverse direction at the base of the forming star.
When the star has collapsed, begin to twist the hexagon on top back again to form the swirls. This is a pretty messy move, but I don’t know any better way to do it. Start with one pleat, fold it back, move to the next exposed pleat, fold it back, and work your way around the hexagon until you have enough slack to twist it and lay it flat (the pleats themselves will not lay flat).
The tessellation contiues by “splitting”or bifurcating the pleats that leave the hex swirl to make triangular twists all around it. Remember, the pleats are three creases wide, so they should be split into two pleats that are also three creases wide. Notice where the splits occur. The triangle twists are done similarly to the swirled hexagonal twists; the twists are not collapsed as simple triangles, but as triangular stars with a smaller triangle on top. The little triangle on top is then twisted back, just as the hexagons were, to make the swirls.
Each pleat around the central hexagon is split with a triangle swirl, and then new hexagon swirls can be formed where the new pleats intersect to make a complete tessellation pattern.
The original images for this tutorial can be seen here. Pictures on flickr can be viewed larger than they are presented here.