Higher-dimensional geometry is the study of shapes and spaces that exist in more than three dimensions. While we are familiar with points, lines, and surfaces in our three-dimensional world, higher dimensions can include additional directions that are difficult to visualize. Mathematicians use abstract concepts and equations to explore these dimensions, which can have applications in fields like physics and computer science. In higher-dimensional geometry, objects such as hypercubes and hyperspheres are examined. A hypercube, for example, is the four-dimensional equivalent of a cube, while a hypersphere extends the idea of a sphere into higher dimensions. These concepts help researchers understand complex systems and phenomena that cannot be easily represented in our three-dimensional space.