A 4D polytope is a geometric shape that exists in four-dimensional space, extending the concept of three-dimensional shapes like cubes and spheres. Just as a cube is made up of square faces, a 4D polytope is composed of three-dimensional "faces," which can be cubes, tetrahedra, or other shapes. These polytopes can be difficult to visualize since humans perceive only three dimensions. However, mathematicians use projections and cross-sections to study their properties. Examples of 4D polytopes include the tesseract, which is the four-dimensional analog of a cube, and the 16-cell, which is a four-dimensional shape made up of tetrahedral cells.