polytopes
Polytopes are geometric shapes that exist in multiple dimensions. The simplest polytope is a line segment in one dimension, while in two dimensions, we have polygons like triangles and squares. In three dimensions, we encounter polyhedra, such as cubes and pyramids. Polytopes can be defined in any number of dimensions, making them a fundamental concept in geometry.
These shapes can be classified based on their properties, such as the number of faces, edges, and vertices. For example, a cube has six faces, twelve edges, and eight vertices. Polytopes are studied in various fields, including mathematics, computer science, and physics, due to their applications in optimization and modeling.