Source: wikibot/balinski-s-theorem
= Balinski's theorem
{wiki=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).