Capturing polytopal symmetries in the edge-graph
- Martin Winter (TU Chemnitz, Chemnitz, Germany)
In general dimension the edge-graph of a polytope carries very little information about the polytope itself. For example, the edge-graph can have many more symmetries than the polytope or any realization thereof.
Using techniques from spectral graph theory and convex geometry we show that the edge-graph of every polytope can be colored so that every combinatorial symmetry of the colored edge-graph extends to a geometric symmetry of the polytope.
Up to now, the only proof known of this fact makes use of spectral graph theory and demonstrates the usefulnes of this seemingly unrelated subject in the study of polytopes.