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 structures that are made up of distinct, separate parts, such as points, lines, and polygons. It often involves counting and combinatorial techniques to analyze these objects. One of the key areas of research in discrete geometry is the study of convex polytopes, which are multi-dimensional shapes with flat sides. Other topics include tiling, graph theory, and combinatorial geometry, which explore how geometric figures can be arranged or combined in various ways.