polytope

A polytope is a multi-dimensional geometric shape with flat sides, generalizing polygons (2D) and polyhedra (3D) into higher dimensions. Think of it as a solid or the shape made by connecting flat surfaces called faces, which meet along edges and vertices. For example, a cube is a 3D polytope with six square faces. In higher dimensions, these shapes become more abstract but follow similar properties: they are bounded, convex sets formed by linear inequalities. Polytopes are important in fields like mathematics, optimization, and computer science for understanding complex structures and feasible solutions.