convex polytopes

A convex polytope is a three-dimensional shape made up of flat surfaces called faces, which connect at edges and vertices. It’s like a multi-sided 3D shape where any straight line drawn between two points inside the shape remains entirely inside it—this is the "convex" property. Examples include cubes, pyramids, and certain more complex shapes. Convex polytopes are fundamental in mathematics and geometry because they help understand the structure of complex shapes and spaces, and have applications in areas such as optimization, computer graphics, and computational geometry.