polyhedral geometry

Polyhedral geometry is the study of shapes formed by flat surfaces, called polygons or polyhedra, in three or more dimensions. Imagine 3D objects like cubes, pyramids, and dodecahedra, which have flat faces, straight edges, and sharp corners (vertices). This field explores their properties, how they can be split or combined, and the relationships between their faces, edges, and vertices. It combines algebra, geometry, and combinatorics to understand complex shapes and structures, with applications in fields like architecture, computer graphics, optimization, and molecular modeling.