lattice polytope

A lattice polytope is a geometric shape in multiple dimensions whose corners (vertices) are located at points with integer coordinates, meaning their positions are described by whole numbers. Think of it as a multi-dimensional "polygon" or "polyhedron" built from points on a grid of integers. These shapes are studied in mathematics because they bridge geometry, algebra, and number theory, providing insight into patterns and structures within discrete spaces. Their regularity and the fact that all vertices lie on the lattice make them useful in areas like optimization, combinatorics, and computational geometry.