Barnette's conjecture

Barnette's conjecture is a proposition in the field of combinatorial geometry, specifically concerning polyhedra. It states that for a polyhedron with \( n \) vertices, the number of faces \( f \) must satisfy the inequality: \[ f \leq 2n - 4 \] This conjecture essentially posits an upper bound on the number of faces in a convex polyhedron based on its number of vertices.