Dave Mitchell's Sonobe Variation "Cyclone"

So here it is. Finally. My version of the diagrams of Dave Mitchell's sonobe variation "Cyclone". I have folded a few modules (like 2000 or so) over the last couple years and still find it a quite pleasing process. So I asked Dave if I could make new diagrams and add a bit of my own sauce to it. 

Of course it is more about colouring than reinventing the wheel. So find here a few words on the diagram and how to distribute colours nicely. The text and images are part of the printed instructions from the DIY Box

So get prepared. I would recommend thin paper naturally, but every paper works naturally. It might need a bit of testing, but I am confident that you find a fitting paper

I recommend 5×5cm paper, the result is then 5.8 cm in diameter. But if you can find only 70g/m² and above, try 7.5×7.5 cm. Kraft paper definitely works good, but is a bit slippery and bulky for 5×5cm. 

For the first unit you definitely need another sheet of the same size folded into fourth. This is a kind of ruler, if you like, to measure the necessary thirds. Yes, there are other methods but I like to keep it simple and this method has been used in carpentry for millenia.

Assembling 30 modules is just like you would do for the usual sonobe unit. A good method is to first assemble a pyramid of three units.  

 

There are several ways to assemble the units. The first most known is the small triambic icosahedron (say that three times fast). It consists of 30 units and is often wrongly named sonobe dodecahedron. In fact it is the second stellation (B2) of an icosahedron for those who want to know. What it really means is just that there are 5 pyramids arranged around a center.

 Finally, the question remains what to do if you wanted to use more than one colour. Popular is the choice of 5 colours, i.e. 6 modules of each colour. Of course, we want all colours distributed nicely. One way to do that is do set up two rules. First, every pyramid consists of three distinct colours. And second, the "windmills" show all five colours. The problem can be reduced to a colouring of the dodecahedron net. At first this seems to be surprising. Earlier we spoke about icosahedron and now it is a dodecahedron? What??

The solution is this. The peaks of five neighbouring pyramids form a pentagon (see image below) in the small triambic icosahedron. In total there are 12 pentagons that form a dodecahedron. Every two peaks are connected by a single module with a specific colour. This means we reduced the colouring  problem of the origami small triambic icosahedron to a colouring problem of the dodecahedron graph. 

And finally here is the solution of the colouring problem for five colours:

 

 

And yes, the final kusudama will look the same back and front. That is the consequence of this special solution here. Do you recognize how the inner and outer pentagon relate colourwise?

There are other solutions of course, but this is the one i prefer just because it is easier to follow and quite symmetric.

 

At the end a small disclaimer. The actual instruction booklet of the DIY-Box contains solutions to colouring problems with 2 and 3 colours, notes on mass production and some more detailed descriptions. Moreover a guide on inlays to make the modules even more colourful.

Diagram with the friendly support of David Mitchell. Visit his site here: Click!

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