Barycentric Subdivision

An operation on a simplicial complex that produces a finer simplicial complex by inserting the barycenter of each simplex and subdividing each simplex into smaller simplices whose vertices are barycenters of faces.

A standard combinatorial operation on simplicial complexes that replaces each simplex by a collection of smaller simplices obtained by joining the barycenter of the simplex to the barycenters of its faces, producing a finer simplicial complex with the same underlying polyhedron.