Gömböc: a 3D body with just one stable and one unstable point of equilibrium

     A gömböc or gomboc is a convex three-dimensional homogeneous body which, when resting on a flat surface, has just one stable and one unstable point of equilibrium. Its existence was conjectured by Russian mathematician Vladimir Arnold in 1995 and proven in 2006 by Hungarian scientists Gábor Domokos and Péter Várkonyi. More information in Wikipedia.

     The gömböc shape is not unique; it has countless varieties, most of which are very close to a sphere and all have very strict shape tolerance (about 0.1 mm per 10 cm). The most famous solution has a sharpened top and is shown on the right. Its shape helped to explain the body structure of some turtles in relation to their ability to return to equilibrium position after being placed upside down. The .slt file of this model can be downloaded from the media repository (source: ThingInverse).