Folding sonobe units effectively

I have to admit that i sometimes get a craze and do some pretty weird stuff with origami. Lately I'm into something that I like to call "Sonobe Carpet", which is nothing but a flat arrangement of, yes, quite a lot of Sonobe units.

The latest outbreak of this insanity (just kidding) produced a large sonobe carpet of about 50cm in diameter and is made from 1,332 units. A lot, right?

And in another craze some really huge sonobe spheres came into being. I mean 30 is standard, but i ended up making spheres with 6, 12, 30, 90, 180 and 210 units. That's a little more than 500 units total. 

 

That's a bit insane, even for my standards. Hehe. Luckily I had the units ready from another project.

Here are the instruction for folding sonobes:

 

 

 

Sonobe Variant Variation

Back then I wouldn't use paper in 15×15 cm directly to fold any unit, neither would i just cut smaller squares. The crucial issue is how to make cutting multiple units from one sheet as effective as possible for the folding afterwards.
The answer is that I analysed the crease pattern of the sonobe module and tried to find lines that i could fold into the big sheet before cutting. This way I would save some steps.
The unit I use frequently is a variant that looks like the one by Tomoko Fuse, but the layers are distributed just a little different to keep the number of layers of paper at bay. However, it turns out that only few lines could be prefolded. That's still a time saver.

Here are two examples, the first one is a variant that you could fold straight away, just subdivide the paper into four on one side and 16 on the other. The resulting squares are 3.75×3.75 cm. For me that's a nice size to work for small and detailed carpets or sonobes. The usual 30 piece sonobe ball is little more than 3.5cm in diameter. 

If you need something more handy and easy to fold, i would recommend going for the 5×5cm version. This way you only get 9 units per sheet.

This is a nice starter size. And if you need really tiny ones, this is the starting point, as subdividing this pattern once more you get a reasonable size unit, still tiny, but not as tiny as if you would do the same thing to the 4×4 version. And good news: this yields 36 units. Enough units for a whole sonobe dodecahedron and a cube from just one sheet of paper. 
That works perfect for thin papers, even standard kami. But if you fold from about 70g/m² upwards I would recommend sticking to the 4×4 plan. The units get very thick otherwise and putting them together will be a real pain. And the result will look messy. Who wants that? Hehe.

But hey, isn't there one problem left? How the hay do I subdivide my paper into three equal parts? The traditional method of just winging it won't bring you much joy, it's just too imprecise. And constructing it with origami methods might be nice from a mathematical viewpoint, but it leaves some stupid crease lines on the paper. 
Indeed, there is a better way to do that. It's a carpenter's trick and has been used since centuries. The earliest source I found was a manual on carpentry from the early 19th century. But how does it go? 
My version is as follows. Take a normal sheet of square paper and subdivide it into fourth. That will be your measuring tape, so to speak. You can keep the reference paper for later and use it again, but here is how you get the trisection:

Trisection of a sheet of origami paper using another one as reference

 The rest is just a matter of repetition. Calculate how many units you need and then prepare the papers. All of them. Otherwise you'll end up going back and fourth cutting and folding. That always tires me quickly.

And for the final process, just a few tips. Lay out 10 units or so (you can increase the number once you have more practice) and then fold 10 times the same step of maximum two folds. Then the next step for all 10 and so forth. You will see how efficient you get after just a few rounds. Now enjoy the stage where you put them all together. My favourite part :D

 

Summary: We did learn how to fold the Sonobe unit and then thought a moment about how to cut prefolded squares with as many useful foldlines as possible. Folding a gazillion units is then just a breeze. Well, not really, but you know what I mean ;)

 

That's it for now. Happy folding and check back soon for more rambling about origami ;)

With best regards, the Valleyfolder

 

PS: Of course the same method works for all modular designs. Fold two or three modules and unfold them completely to reveal the crease pattern. Put them side to side (one right and one on the bottom for example) and then have a go and try to find as many lines that continue over between the sheets as possible. These are the lines that you can prefold before cutting.

Here are two more examples. The first one is for the cyclone Sonobe variation by Tadashi Mori (you find a tutorial on that on YouTube). The second one is what I use to fold the little boxes for my 5×5 cm paper. These boxes are called Glynn-Boxes. You also find tutorials for that on YouTube.com.

Precreasing sonobe cyclone units

Sonobe Cyclone Tutorial: Klick!

precreasing glynn boxes

Glynn-Box Tutorial: Klick!

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