Discrete geometry is a branch of mathematics that studies geometric objects and their properties in a discrete setting. This means it focuses on shapes and configurations made up of distinct, separate points, lines, and polygons, rather than continuous forms. It often involves the analysis of arrangements, distances, and combinatorial properties of these geometric structures. One key area of discrete geometry is the study of convex polytopes, which are multi-dimensional shapes with flat sides. Researchers also explore topics like tiling, graph theory, and combinatorial geometry, which examine how shapes can fit together or how points can be connected in various ways.