Swirly tessellation

swirl tess

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

swirl tutorial 1

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.

swirl tutorial 2

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).

swirl tutorial 3

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.

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4 thoughts on “Swirly tessellation

  1. That back twist is impossible if you keep twisting until the bottom closes. Lost a 48-crease hexagon to that mistake.

    A question: any tips on getting very precise crease intersections? I could use some help there.

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    • I’m not sure exactly what you did, but the hexagonal twist is closed on the bottom, if that is what you are referring to. It is a compound twist; the triple wide pleats are collapsed into a double wide hex twist and a counter-rotating single wide hex on top but both twists are closed. But perhaps you’re referring to something else.
      When folding a grid, I divide the paper just a few times in one direction and the same amount in a second direction and then dividing in the third direction, I am very careful that the creases intersect exactly. If the first set of intersections line up as they should, then you only need to continue dividing the spaces in half exactly and all succeeding creases will intersect as well.

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      • My mistake was that I tried to accomplish the swirl in one single hexagon twist, and of course the paper will not twist that far without the use of a compound twist, as you mentioned. While I was trying to figure this out, I stumbled upon Yureiko’s solution to this compound twist (which can be found in her Flickr page, here: http://www.flickr.com/photos/24776310@N04/2862277310/sizes/o/in/photostream/), and it works fine.

        Also, while I was getting there, I managed to accomplish the compound twist in a way that, oddly, I can’t seem to reproduce: the single hexagon twist sits atop another single hexagon twist, which results in the “arms” of the helix being only two pleats wide. I put a photo comparing both swirls in my Origami album in Facebook, here: https://www.facebook.com/photo.php?fbid=500521063296694&set=a.471958666152934.124779.100000164152883&type=3&theater.

        Thank you very much for the precision tips. I’ll definitely try them out. I’ve been getting a little better with each tesselation, and your method will surely accelerate my progress.

        Have a great weekend!

        Ruy

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