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The Self-Righting Object Answered

The Gomboc is a "mono-monostatic" object -- a three-dimensional object that purely by dint of its geometry has only one possible way to balance upright.

The challenge intrigued two scientists, Gabor Domokos and Peter Varkonyi, both of the Budapest University of Technology and Economics. They spent a few years doing the math, and it seemed as if a mono-monostatic object could, in fact, exist. They began looking to see if they could find a naturally occurring example; at one point, Domokos was so obsessed that he spent hours testing 2,000 pebbles on a beach to see if they could right themselves. (None could.)

After several more years of scratching their heads, they finally hit upon a shape that looked promising. They designed it on a computer, and when it came back from the manufacturer, they nervously tipped it over, wondering if all their work would be for naught. Nope: the Gomboc performed perfectly. "It's a very nice mathematical problem because you can hold the proof in your hands, and it's quite beautiful," Varkonyi says.

It's apparently similar to the shape of tortoise and beetle shells, explaining why these creatures can actually flip themselves back over.


The formula for the Gömböc is published, someone should be able to make one with a printer. That said, the tolerances are very, very critical. I doubt you could make a plastic one that would have exactly two states, but could get close.

So it is!

I wonder if any of the codemonkeys reading this know how to turn that into something a Makerbot could handle?

That's what I am hoping for. In fact, making one that has only two states is very challenging, which is why they are so expensive.

It will not be enough to just program up the formula into 3D object software and print. I speculate that there will need to be some trial and error and then some careful and precise finishing work afterward.

Oh, and forget scanning one.

Why forget scanning one? A photoreal mesh with lots of polygons should be able to render this nicely.

I don't think it would be adequate for the tolerances required, but please prove me wrong!

Oh, 'nother problem is that you have to have one to scan ;-)

can you buy one?

If you check the website I linked to, there's a limited number of them for sale in a hideously-expensive-looking presentation set, limited to 2007 units.

They apparently got it fabricated by Objet/PolyJet printing technology, so there are probably files somewhere for reproducing it in greater and cheaper numbers.

There's a clearer view of the shape on Wikipedia - it looks just the sort of shape you could fiddle with, carve one in stone and polish it with years of fondling.

Thats... awesome!