Scientists Build Real-Life “Loaded d4”

Scientists Build Real-Life “Loaded d4” That Always Lands the Same—Solving a 40-Year Geometric Puzzle

A team of researchers has done the impossible: they’ve created a real-world version of a “loaded” four-sided die—a pyramid-shaped object that always lands on the same face, no matter how it’s tossed. Known officially as a monostable tetrahedron, this geometric oddity, nicknamed Bille, brings to life a decades-old theory first proposed by legendary mathematician John Conway. For tabletop gamers, it’s like holding a cursed d4 that never rolls fair—because it physically can’t.

A d4 That Always Rolls a 1?

Unlike your standard d4 used in Dungeons & Dragons—which has four triangular faces and rolls unpredictably—Bille has only one stable resting face. Toss it, spin it, flip it, or drop it: it always returns to the same orientation. In gaming terms, this is a die with a permanent bias, forged not by trickery but by mathematical precision and high-level engineering.

Conway originally theorized this strange die in the 1980s—a tetrahedron with an asymmetrical weight distribution that would always land the same way. He eventually shelved the idea due to angular momentum issues, noting it was like a car trying to get over a speed bump: movement made it unpredictable. But the concept remained tantalizing, especially for mathematicians and physicists who wanted to crack the code of geometric balance.

Rolling with Precision: The Engineering Behind Bille

Fast forward to a team of modern-day scientific adventurers—Hungarian mathematician Gábor Domokos, his student Gergő Almádi, and long-time tetrahedron tinkerer Robert Dawson. Together, they resurrected Conway’s abandoned idea and finally built the perfectly imbalanced d4.

Almádi’s engineering masterpiece uses carbon fiber for a super-light frame and tungsten carbide for a heavy base, carefully calibrating mass, density, and glue placement (yes, even the glue mattered). During testing, even a tiny blob of adhesive disrupted the effect. Once removed, Bille performed flawlessly—always landing on “Side 1”, no matter what.

Critical Innovation: What It Means Beyond the Game Table

While Bille might sound like a rogue player’s dream die, its implications go far beyond game night. The object’s single-stable equilibrium could revolutionize real-world design, from spacecraft that self-right after landing to pill capsules that orient themselves inside the stomach (as seen with the gömböc, another one-of-a-kind shape previously discovered by Domokos).

In fact, the failed lunar landing by Intuitive Machines’ Athena lander might have been avoided if the lander had a shape—or internal weight system—similar to Bille. A d4 that never tips over might sound like a dungeon master’s nightmare, but in aerospace, it’s a dream come true.

The gömböc, discovered in 2006, can stand on only two points, one stable, the other unstable.

Not for Sale…Yet

Though a second version of Bille was constructed to confirm its behavior, the process is nearly impossible to reproduce without access to the original design specs. So for now, your d4s remain delightfully chaotic—but science has proven it’s possible to make one that always “rolls a 1.”

Domokos summed up the journey: “Bille didn’t just prove a theory—it showed how geometry, physics, and engineering can come together to solve problems and inspire unexpected innovations. And sometimes, they even roll a nat 20 for ingenuity.”