This New Pyramid-Like Shape Always Lands With the Same Side Up

The article discusses a longstanding mathematical problem concerning the tetrahedron, one of Plato’s five polyhedra, specifically whether a tetrahedron made of uniform material can be constructed to rest stably on only one face. In 1966, mathematicians John Conway and Richard Guy proved that a uniformly weighted monostable tetrahedron—one that always lands on the same face—is impossible. However, the question remained open if uneven weight distribution was allowed. While roly-poly toys achieve similar behavior through weighted bottoms, such effects are well understood only for smooth or rounded shapes, not for polyhedra with flat faces and sharp edges. In 2023, Gábor Domokos and his collaborators, including graduate students and Robert Dawson, resolved this problem by proving that a tetrahedron’s weight can indeed be distributed unevenly to create a shape that always lands on the same face. They went further by constructing the first physical model of this “monostable” tetrahedron, made from lightweight carbon fiber