Convex polytope

A convex polytope is a three-dimensional shape formed by flat surfaces, or "faces," where any straight line drawn between two points inside or on the shape stays entirely within it. Think of a cube or a pyramid—these are examples of convex polytopes. They are characterized by being "convex," meaning no indentations or holes, and "polytope," indicating they are multi-faceted, composed of flat polygonal faces. These shapes are important in math, optimization, and computational fields because they can represent feasible solutions or constraints within a bounded, well-structured space.