Tetrahedron Always Lands on One Face

Researchers proved and built a tetrahedron that always rests on one specific face regardless of how it is placed.

They used computer algorithms to identify tetrahedron shapes with obtuse edge angles and defined four small ‘‘loading zones’’ for the center of mass to achieve monostability.

The physical model is made of a hollow carbon fiber frame with a dense tungsten carbide insert, engineered to within 0.1 gram and 0.1 millimeter precision.

The work confirms John Conway’s decades-old conjecture about weight-shifted monostable tetrahedra.

This discovery highlights the role of experimentation in mathematics and could inform designs for self-righting spacecraft.