So it might be surprising that, millennia later, mysteries still surround even the simplest shape in Plato’s polyhedral universe: the tetrahedron, which has just four triangular faces. One major open problem, for instance, asks how densely you can pack “regular” tetrahedra, which have identical faces. Another asks which kinds of tetrahedra can be sliced into pieces that can then be reassembled to form a cube. If you were to place such a “monostable” shape on any of its other faces, it would always flip to its stable side. A few years later, the duo answered their own question, showing that this uniform monostable tetrahedron wasn’t possible.