Theorem of McMullen

McMullen's theorem pertains to the geometry of convex shapes, specifically how they can be structured and characterized through a concept called "mixed volumes." In simple terms, it provides criteria to determine when a set of measures (called mixed volumes) can be realized as the sizes of intersections of convex bodies. This theorem is fundamental in convex geometry and helps mathematicians understand and classify how different convex shapes combine or relate volume-wise, offering a deep insight into the complexity and structure of multidimensional shapes and their interactions.