four-dimensional polytopes

Four-dimensional polytopes, also known as 4D shapes or polychora, are the four-dimensional analogs of three-dimensional polyhedra. Just as a cube is bounded by six square faces, a 4D polytope is bounded by three-dimensional "faces" called cells—such as cubes, pyramids, or other polyhedra. These shapes exist mathematically in four-dimensional space, which is impossible to visualize directly but can be understood through projections and models. They help us explore and understand complex structures beyond our usual three-dimensional experience, playing a role in fields like mathematics, physics, and computer science.