TECH NEWS – Researchers at the Budapest University of Technology and Economics (BME) have achieved what was once thought impossible: the creation of a monostable tetrahedron, a geometric body that could revolutionize the design of landing modules for space missions. Dubbed the “Bille,” this new solid provides proof for a decades-old mathematical conjecture.

On June 25, 2024, BME unveiled the world’s first four-faced object that, like a “roly-poly toy,” always tips back to the same face when placed on a horizontal surface. Working in collaboration with HUN-REN researchers, the team not only designed but physically constructed this unique solid. Their achievement confirms a 1984 conjecture by mathematician John Horton Conway. The project was carried out by Gergő Almádi (architecture student), Gábor Domokos (co-discoverer of the Gömböc and BME professor), and Conway’s former student Robert Dawson (St Mary’s University, Halifax).

The significance of this discovery is that the methods developed can stabilize many spatial shapes using purely geometric means—preventing them from tipping over. The fewer faces a polyhedron has, the harder this is to achieve. Until now, most believed it impossible for a four-faced solid (tetrahedron) to have this property, but the Bille is just such a creation, built with a lightweight carbon tube frame and a dense tungsten carbide core for perfect balance.

“There’s no harder puzzle in this field: if this is possible, our principles could be applied to any polyhedron, regardless of the number of faces,” said Gábor Domokos. He emphasized that the Bille opens up a new avenue for geometric construction, and engineers will have to explore how to put this approach to practical use. For instance, as he noted, there are currently three disabled landers lying on their sides on the Moon—this solution could help prevent such outcomes.

“Solving the geometric problem of the Bille could inspire new designs for self-righting structures, such as future space landers,” explained the professor. He added that while a mathematical proof can be found faulty, “this cannot be, as the model works in the real world.”

The study on the Bille will be published in Quanta Magazine on June 25. The preprint version is available here: Building a Monostable Tetrahedron (Gergő Almádi, Robert J. Macg. Dawson, and Gábor Domokos).