A 4D polytope is a geometric shape that exists in four-dimensional space, extending the concept of polygons (2D) and polyhedra (3D). Just as a cube is a three-dimensional version of a square, a 4D polytope can be thought of as a higher-dimensional analogue. These shapes can have various properties, including vertices, edges, and faces, but they also include additional features unique to four dimensions. One common example of a 4D polytope is the tesseract, also known as a hypercube. A tesseract has eight cubical cells, and its structure can be difficult to visualize since humans perceive only three dimensions. Mathematicians study 4D polytopes to explore concepts in higher-dimensional geometry, which can have applications in fields like physics and computer science.