Exhibit: Barycentric refinement

In the following picture, the Barycentric refinement was done the classical way, using the coordinate embeddings starting with a pentagon. The refinement is abstractly defined for any graph without using any Euclidean coordinates: take all complete subgraphs as vertices and connect two such subgraphs, if one is contained in the other. See the article, where we prove a universal spectral behavior of such graphs.