What is "gomboc"

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. 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 100 mm).

The most famous solution has a sharpened top, as shown in the photo. Its shape helped to explain the body structure of some tortoises in relation to their ability to return to equilibrium position after being placed upside down. Copies of gömböc have been donated to institutions and museums, and the biggest one was presented at the World Expo 2010 in Shanghai, China.