Higher-dimensional polytopes are geometric shapes that extend the concept of polygons and polyhedra into more than three dimensions. While a polygon is a flat shape with straight sides in two dimensions, and a polyhedron is a three-dimensional shape with flat faces, higher-dimensional polytopes exist in four or more dimensions. These shapes can be studied mathematically and are often represented using coordinates in higher-dimensional space. One common example of a higher-dimensional polytope is the tesseract, which is the four-dimensional analog of a cube. Just as a cube has six square faces, a tesseract has eight cubic cells. Higher-dimensional polytopes are important in various fields, including mathematics, physics, and computer science, as they help in understanding complex structures and theories.