A New Pyramid-Like Shape Always Lands the Same Side Up

Summary

Achieving the right balance between the weight of the loading zone and the weight of the rest of the tetrahedron is easy in the abstract realm of mathematics — you can define the weight distribution without a care for whether it’s physically possible. You might, for instance, let parts of the shape weigh nothing at all, while concentrating a large amount of mass in other parts. But that wasn’t entirely satisfying to the mathematicians. Almádi, Dawson and Domokos wanted to hold the shape in their hands. Was it possible to make a monostable tetrahedron in the real world, with real materials? Getting Real The team returned to their computer search. They considered the various ways in which monostable tetrahedra might tip onto their stable face. For instance, one kind of tetrahedron might follow a very simple path: Face A tips to Face B, which tips to Face C, which tips to Face D. But in a different tetrahedron, Face A might tip to Face B, and both Face B and Face D will tip to Face C. The loading zones for these different tetrahedra look very different. The team calculated that to get one of these “falling patterns” to work, they would need to construct part of the shape out of a material about 1.5 times as dense as the sun’s core. While studying to be an architect, Gergő Almádi was drawn to a decades-old geometry problem. They focused on a more feasible falling pattern. Even so, part of their tetrahedron would have to be about 5,000 times as dense as the rest of it. And the materials had to be stiff — light, flimsy materials that could bend would ruin the project, since it’s easy to make a round or smooth shape (like the roly-poly) monostable. In the end, they designed a tetrahedron that was mostly hollow. It consisted of a lightweight carbon fiber frame and one small portion constructed out of tungsten carbide, which is denser than lead. For the lighter portions to have as little weight as possible, even the carbon fiber frames had to be hollow. With this blueprint i...