polyhedral theory

Polyhedral theory studies shapes called polyhedra, which are three-dimensional figures made up of flat faces, straight edges, and sharp corners (vertices). Think of common objects like cubes or pyramids. Mathematically, these shapes can be described using linear inequalities, which define a region of space containing all possible points that satisfy those inequalities. This theory helps in areas like optimization, where it’s used to find the best solution within certain constraints, by analyzing the geometric structures formed by these inequalities. Overall, polyhedral theory provides a way to understand and work with complex shapes defined by linear rules.