Polytopes in four or more dimensions are geometric shapes that extend the concept of polygons and polyhedra into higher dimensions. While a polygon is a 2D shape with straight edges, and a polyhedron is a 3D shape with flat faces, polytopes can have any number of dimensions. The simplest example of a polytope in four dimensions is the tesseract, which is the four-dimensional analogue of a cube. These higher-dimensional polytopes can be difficult to visualize, but they can be studied mathematically using projections and coordinates. Just as a 3D object casts a 2D shadow, polytopes in four or more dimensions can be represented in lower dimensions to help understand their properties.