Regular polytopes

Regular polytopes are highly symmetrical, multi-dimensional geometric shapes where all sides and angles are identical. In simple terms, they are the generalizations of regular polygons (like equilateral triangles and squares) into higher dimensions, such as regular polyhedra (like cubes and tesseracts). These shapes exhibit uniformity in their structure, with each face, edge, and vertex sharing the same properties and arrangements. They are studied in mathematics because of their symmetry and beauty, and they help us understand the geometric properties of shapes beyond three dimensions.