Gömböc

by James Buckland

A Gomboc is a wild little thing, a weeble with constant density. Weebles, also known as roly-poly men in some countries, are children’s toys shaped like eggs, with a weight at the bottom so that, when pushed over, the toy will right itself. This works from virtually any position — the density gradient and the smooth shape ensure that the weeble will return to the upright position from any possible placement.

Mathematically, this can be described as a monostatic polytope, a shape that has instability on all but one of its faces — that is, it’s unstable enough to right itself from all placements but one. This is a terribly hard field of study, and in 2006, a Hungarian team of scientists — Gábor Domokos and Péter Várkonyi — found the Gomboc, a three-dimensional mono-monostatic polytope, a shape with constant density (instead of being weighted, like a weeble) that will roll, wobble, and right itself from any position whatsoever. It works by the same principles — the relation between the object’s center of mass and its proximity to the surface of the object lead it to trace a path of contact with the ground which will, eventually, find itself upright.

Perhaps without coincidence, this Gomboc (meaning little sphere in Hungarian) is not too dissimilar from another shape known for righting itself — turtle shells. In fact, as part of their research into the properties of the then-theoretical Gomboc, the duo spent time in Budapest measuring turtle shells for their properties. They visited pet shops, the Budapest zoo, and the Hungarian Museum of Natural History; they took careful geometric measurements of the shells. Nature did get there first.

In fact, it is not unprecedented for nature to find employment for the geometric shapes of objects. The traditional elongated-oval shape of an egg, for instance, evolved in such a way that, when set adrift, the egg will only trace small, tight circles, instead of rolling far away from the nest. Red blood cells in mammals have a similar property — their disc-torus shape allows increased laminar flow, as well as more surface area.

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