Klein quadric

The Klein quadric is a geometric construct in higher-dimensional space that represents all lines in three-dimensional space as points on a special surface called a quadric. Imagine translating every line in 3D into a single point in a 4D space, where these points form a smooth, curved surface (the Klein quadric). This representation allows mathematicians to study the relationships and intersections of lines in space through geometric properties on this surface. It provides a powerful way to analyze complex configurations of lines using the tools of algebra and geometry.