Mathematicians Solve 60-Year-Old Mystery of the Monostable Tetrahedron
A unique tetrahedral design may hold the key to advancements in the space industry and mobile robotics. Here’s what makes it so extraordinary.
Meet Bille—the world’s first monostable tetrahedron, a four-sided object that always lands on the same face, regardless of its initial position. This long-awaited discovery solves a mathematical riddle that has puzzled engineers and architects for nearly 60 years. Bille could influence the future design of autonomous spacecraft for lunar and planetary missions, Phys.org reports.
The concept was first proposed in 1966 by renowned British mathematician John Horton Conway and his colleague Richard Guy. They questioned whether a tetrahedron made from a uniform material with even weight distribution could return to the same position each time it was moved. While they believed it was theoretically possible, they were unable to demonstrate it.
The problem remained unsolved until Professor Gábor Domokos of the Budapest University of Technology and Economics (BME) and his team applied advanced computational modeling to find a solution. Their research revealed that a true monostable tetrahedron must be mostly hollow inside, with one face significantly denser than the others—by thousands of times.
With support from a Hungarian precision engineering firm, the team created the first physical prototype. It consists of lightweight carbon fiber tubes and one side made of a high-density tungsten carbide alloy. Measuring half a meter across and weighing 120 grams, the design was named “Bille,” a Hungarian word meaning “to tilt.” Regardless of the starting position—whether side A, B, C, or D—Bille always settles on side D.
The potential applications are significant. In space exploration, such a structure could improve lander stability, reducing the risk of accidents like the failed landing of the Athena probe in NASA’s IM-2 mission. That mission ended in failure when the module tipped over after falling into a crater.
Bille’s discovery offers a new approach to engineering and design—where balance and stability are built into the shape itself.