Domokos spent most of his career at the Budapest University of Technology and Economics (BME), where he received his MSc degree in architecture and engineering in 1986, and defended a PhD in 1989 and habilitation in 1996.
In 1995 he met the prominent Russian mathematician Vladimir Arnold, who suggested that 3D mono-monostatic bodies do exist and urged Domokos to find one.
In one experiment, the couple tried 2000 pebbles collected at the beaches of the Greek island of Rhodes and found no single mono-monostatic body among them, illustrating the difficulty of the problem.
In 2006 Domokos and his student Péter Várkonyi theoretically found a stable class of mono-monostatic solutions,[2] which they named gömböc (a diminutive of gömb meaning a "sphere" in Hungarian).
[4] On 13 February 2009, a gömböc appeared on BBC One Friday night show QI, where the host Stephen Fry demonstrated its properties and Domokos, who was present in the audience, explained its history and relation to turtles.