Fold your own tessellation | MIT Technology Review
Download the pattern for Dancing Ribbons here.
Yoder recommends printing the pattern on paper in between normal printer paper and cardstock in weight, making sure it folds in straight lines (not too thick), folds back and forth easily on the same line (not too thin), and is crisp enough to make a satisfying snapping noise when you shake it. Her favorite paper isSkytone, which is commonly used to print certificates and fancy envelopes.
Watch the video tutorial on folding Dancing Ribbons here.
Yoder’s detailed folding instructions:
Once you have your crease pattern on a sheet of paper, cut out the hexagon that contains the pattern. Yoder recommends using a straightedge and blade on a cutting mat instead of scissors, whether that means an X-Acto knife and a ruler on a sheet of cardboard or a quilting ruler and rotary cutter on a fabric cutting mat.
The next step is folding the background grid of black lines that the pattern uses as references. Assuming you’ve cut out your hexagon precisely, you can use the edge of the hexagon and the printed lines to make your creases, or you can fold as if there were no lines printed by folding the hexagon in half (edge to opposite edge) and then folding those edges in to the center to make quarter lines, first in one direction and then in the other two. After each set of folds, it’s a good idea to fold the new lines back the other way to make the paper easier to work with later. After folding the quarters, fold the eighths in each direction, and finally the 16ths. Yoder presses the creases with a bone folder to make them easier to work with and to minimize stress on her hands.
You can choose at this point whether to fold the pattern one twist at a time or to precrease the off-grid creases (just crease the short segments that have been printed, folded as mountains on the printed side of the pattern) and collapse everything all at once. Beginning folders may find it helpful to precrease the triangle and rhombus twists, to make the squashing process easier, even if you plan to fold the pattern one twist at a time. Solid red lines in the crease pattern represent mountain folds, and dashed blue lines represent valley folds. The faded lines inside the twists are helper folds used to set up the twists; they will not be used in the final pattern.
The central closed hexagon twist will be the first twist folded, and it’ll be made on the blank side of the paper. All the mountain folds for this twist (as viewed on the blank side of the paper) will be on grid lines going to the corners of the hexagon, and the valley folds will be one grid spacing above the mountains on the right-hand side of the paper. To fold the twist, set up both the mountain and valley folds of one pleat; then pass that pleat counterclockwise into your other hand before setting up both folds of the next pleat. Keep all pleats folded and the center of the paper elevated as you work your way around the center, eventually folding all six pleats (use your table to keep the pleats folded, or use clips at the edge of the paper) and forming a hexagonal tower in the center of the paper. Make the pleats more flat, working from the edges in, until this hexagon tower is two grid spacings high. Then grab the tower and give it a sharp counterclockwise twist to get it to lie flat. This twist almost never lies down completely flat right away, so lift each pleat slightly to make sure the valley folds have stayed on grid lines to help the central hexagon to smooth out.
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