Sonobe Balls

Recently, I acquired an obsession over Sonobe modulars. In my quest to find the perfect origami holiday gift, I came across the Sonobe ball. It’s easy but not effortless, it’s sturdy and won’t fall apart, and its simple beauty can be easily appreciated by non-origamists.

Figure 1: Stellated Octahedron: 12 Sonobe Units, 4 Pyramid Units

Figure 2: Stellated Icosahedron: 30 Sonobe Units, 10 Pyramid Units

I usually prefer more “complex” origami, but Sonobe balls, as simple as they seem, have complexities too. The standard Sonobe ball with outward pointing pyramids was cool and all, but what happens if you invert the pyramids?

Figure 3: Inverted Stellated Icosahedron: 30 Sonobe Units, 10 Pyramid Units

It works, but a couple challenges arise. First, when inverted, the pockets for assembling the Sonobe ball move from the outside to the inside of the ball, which makes assembly of the final unit considerably more difficult. A quick modification to each individual unit will reverse the pockets back to the outside again, but I opted to stick with traditional unit.

Figure 3: Zoom on Figure 4. Look at this ugly hole.

The bigger problem is that the inverted ball looks ugly, as the thing is full of awkward holes. Of course, these holes were partially caused by my hasty folding, but I’m more concerned about the theoretical change in the way the ball is held together. In all modular models, units “want” to fall out of their pocket (some refer to the pockets as locks). Friction helps prevent the unit from falling out, but the main force holding a unit in place is its cohesion the rest of the units. If we imagine the falling out of each piece to be a force vector, the sum of all of the force vector in a modular origami model is zero. Each unit might want to fall out due to its own force vector, but its own force vector helps keep its neighboring units in place.

Figure 5: uninverted Sonobe ball with “force vectors”

Now, if we look at the inverted Sonobe ball with this force vector model (Figure 5), it quickly becomes clear why it has big, ugly holes when its uninverted sibling doesn’t. First, we can notice that although Sonobe balls are made with Sonobe units, they can also to be seen as made up of many “pyramid units”, where each pyramid unit is formed by three Sonobe units. Then, when we look at the holes where pyramid units intersect, it can be seen that, in the uninverted Sonobe ball, the force vector point towards the hole. In other words, they actively “try” to close the hole. On the other hand, the force vector in the inverted Sonobe ball point away from the hole, so they actively “try” to make the hole bigger.

Figure 6: inverted Sonobe ball with “force vectors”

I never actually got around to solving this problem for the inverted Sonobe ball. Better paper and more careful construction could probably do the trick, but a modification in design sure would be cool. The “force vector model” isn’t only useful for Sonobe balls, it can be applied to other modular origami as well. I have never come across anybody describing modular origami in this way, so I hope you will find it useful in your own modular origami adventures.