Barycentric subdivision

Barycentric subdivision is a technique used in the field of algebraic topology and geometry, particularly when working with simplicial complexes and triangulations. It involves a process that refines a simplicial complex by adding additional vertices and simplices based on the original structure. Here’s how barycentric subdivision works in detail: 1. **Starting Structure**: Begin with a simplicial complex, which is a collection of simplices (points, line segments, triangles, etc.) that satisfy certain properties.