lattice polytopes

A lattice polytope is a geometric shape in multi-dimensional space made up of points with integer coordinates, meaning each point's position can be described using whole numbers. Think of it as a multi-sided shape (like a polygon or polyhedron) whose corners are defined precisely on a grid of points with integer values. These shapes are studied in mathematics because they combine geometric structure with number theory, and they have applications in optimization, algebra, and computational geometry. Essentially, lattice polytopes are the "digitally aligned" shapes that help mathematicians understand complex multi-dimensional spaces and problems.