volume of lattice polytopes

The volume of a lattice polytope measures how much space it occupies within a grid of evenly spaced points (like points on a graph). Unlike regular volume, which can be fractional, lattice volume is scaled so that a basic unit cube (1×1×1) within the grid has volume 1. This means the lattice volume counts how many of these unit cubes fit into the polytope, considering its shape and position on the lattice. It's a way to quantify the size of shapes with corners at grid points, linking geometric size to the underlying lattice structure.