“...the enjoyment derived from a puzzle is proportional to the time spent on it.”
These instructions are still a work in progress. In the video below I demonstrate the basic approach to folding these pieces, but I plan on converting select highlights of the video into gifs and organizing them better along side the written instructions on the right side of this page. Apologies if this inconveniences anyone—please leave a comment if you have any questions! Also check out the gallery of curved-crease objects for more work.
Start by removing the center from the piece: using your index fingers and thumbs, gently pressure your fingertips against one another until each tab snaps apart — you may hear a quiet snapping noise.
Next, slide your fingertip across the surface of the material to determine which creases are on which side — you should be able to see the crease pattern from both sides of the material, but you'll only feel the score from the side it was etched on. The score always goes into the trough of the fold, this helps prevent the laminate from peeling away from the foil.
Once you know which side the crease belongs on you can bend the material very far — the foil & laminate material is very forgiving and does not crinkle easily — with your index finger and thumb pressing down on the “mountain” side, and your middle finger in-between them on the “valley” side, you can slide the piece around it's circumference, leaving behind a natural bend in the material’s crease. (That is, letting go of the material you'll see a distinct bend remaining.)
Information on Curved-Crease Folding
Curved-crease folding is difficult: it requires patience & persistence (and a laser beam is really handy too). Several factors can influence the difficulty of folding curved crease origami, most importantly the crease pattern itself, and the material used. Pre-creasing the material with a laser provides tremendous benefits, though a knife, a ball-point pen, or a spring-loaded ball burnisher all work as well.
The materials I've used, in order of descending difficulty, are: heavy paper (≥65lb), two sheets of thin neon paper on either side of a double-sided adhesive sheet, two sheets of thin foil wrapping paper on either side of a double-sided adhesive sheet, and a single sheet of thin foil wrapping paper coated on both sides with self-adhesive laminating sheets. (And I've seen other work in a variety of plastic-like materials as well.)
Folding with paper, even with a pre-crease provided by a laser, is incredibly tedious, often taking several hours to slowly increase the crease angle, until eventually the whole pattern suddenly “pops up”, at which point it tends to get much easier — even the slightest mistake can leave undesirable kinks that can interfere with the pattern folding up properly. The foil & laminate materials are far more forgiving, being very difficult to crinkle unintentionally.
In all of the annular (donut-shaped) patterns, the hole in the middle of the pattern allows the material to be folded “through” itself, which allows for a great deal of variation in the final result.