Balinski's theorem

Balinski's theorem is a result in the field of combinatorics and relates to the properties of convex polytopes. It states that every polytope in \( \mathbb{R}^d \) that is simple (meaning each vertex is the intersection of exactly \( d \) faces) can be decomposed into a fixed number of simplices (the simplest type of polytope, generalizing the concept of a triangle in higher dimensions).