"In 1966, John Conway and Richard Guy explored whether a uniform tetrahedron could sit on one face only; they later proved it was not possible. Be it evenly distributed weight, generating a consistent balance is elusive in polyhedra."
"Initially, it might seem that an uneven weight distribution would allow for a monostable tetrahedron. However, this idea only applies to smooth or round shapes, not to the sharp edges and flat faces of polyhedra."
Plato's concept of polyhedra includes the tetrahedron, which remains a focus of mathematical inquiry. Key open questions involve packing density and the feasibility of slicing tetrahedra into cubes. John Conway and Richard Guy's 1966 work questioned the existence of a uniformly weighted tetrahedron that could sit only on one face; they proved its impossibility. Uneven weight distribution might seem a potential solution, but this conceptual approach falters with the edges and faces of polyhedra, complicating design viability for consistent balance.
Read at WIRED
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