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

Plato envisioned the cosmos as an arrangement of five geometric shapes called polyhedra.

The tetrahedron, which has just four triangular faces, is an important object of mathematical study.

But it's not clear how to design something that will always flip to the same side of a polyhedron.

In 2023 , Gábor Domokos , a mathematician at the Budapest University of Technology and Economics , proved that it is indeed possible.

A team of Hungarian mathematicians created a monostable tetrahedron in the real world.

They used computer technology to create a model of the shape that didn’t work at all.

The team designed a lightweight carbon fiber frame and one small portion constructed out of tungsten carbide.

The monostable tetrahedron is the kind of problem that’s often easiest to overlook.

It's not clear what new theoretical insights the model will provide, but experimenting with it might help mathematicians uncover other intriguing questions.

In the meantime, Domokos and Almádi are working to apply what they learned to help engineers design lunar landers that can turn themselves right side up after falling over.