11/10/2023 0 Comments Modular origami 30 unitsI'm not sure which torus I saw first or where I saw it, but when I was starting this project I searched for more information and found this website with some good instructions and recommendations: I did not come up with the idea in the first place - I saw a picture of another Torus and wanted one for myself. Unfortunately this link has since stopped working.Īt the bottom of this page I included a schematic which would have helped me a bit more than the schematic at the above website. I used paper that was about 3 inches square, and ended with a torus that was about 16 inches in diameter.Īlso, if you want to make your own torus I have a few of my own recommendations: I was able to do it with their schematic - but I had a little trouble. If they are perfectly square it will make the rest of the process easier! There are a lot of squares to cut, but don't rush them. Some splaying will happen, but any sloppiness translates into the final torus. I would not suggest cutting a square, folding the unit, and then cutting another square. I first cut all the squares, then I folded all the units - even breaking that up into stages. This might make it more tedious, but I think it helped make the final model more consistent. There are a couple really nice color schemes out there for this model, it certainly looks elegant in a single color. I've also seen a rainbow pattern which looks really cool. I wanted something a little bit bit different to go with the elefantenhaut paper I wanted to use, so I set out to find a three coloring. The graph which is formed by the individual PHiZZ units is a 3-regular graph, in that each vertex has exactly 3 edges leaving it, so we know that it can be edge colored in at most 4 colors. To find the 3 coloring I folded a test one (yeah, an entire test torus out of just regular printer paper.), labeled the vertices / edges, and worked out the graph on a sheet of paper. I used the fact that the graph has 12 fold rotational symmetry and I encoded 1 / 12 of the three coloring as a SAT problem and solved it with glucose. Oh yeah, I also made a quick visualization of the graph: There are more efficient ways of solving three colorings, but this was fun. I used Zanders Elefantenhaut which is a book binding paper. It is relatively thick for origami but is really good for wetfolding, tesselations, or this sort of modular origami. It is nice and crisp, holds a fold really well, and doesn't crack. I used a big straightedge and an xacto knife to cut the squares. The cutting actually took a long time because I wanted to be relatively accurate, so I only cut through one sheet at a time. Now folding, first I did all the 'accordions'. Two pictures for hours and hours of work spread out over several weeks. This is the only picture I have from the final assembly - got on a bit of a roll! They slot together without any tape or glue which is nice. It should be noted that the units above can be assembled into many forms including a 12-unit cube, a 30-unit stellated icosahedron, a 60-unit spiked pentakis dodecahedron, a 90-unit dodecahedral model, and even larger assemblies.I started with the inner 12 hexagons which was by far easiest, then all the heptagons, then the pentagons, and then finally all the remaining hexagons to close it out. Swan Sonobe: this unit is so named because the assembled models have a pattern which looks like the head and neck of an origami bird. Striped Sonobe: Obvious from its name, this origami unit forms striking stripes. Snow-Capped Sonobe 1: When assembled, the white parts of the paper converge at the corner giving the appearance of snow at the peak of mountains. When assembled, units form a white (back side of origami paper) pinwheel pattern, or a daisy pattern. Mukerji modified the original Sonobe Unit to generate pleasing variations.ĭaisy Sonobe. Section 1: Sonobe VariationsMitsonobu Sonobe designed an easy-to-fold and versatile origami unit called the “Sonobe Unit”.
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