Symmetric (co)homology polytopes

A common idea in many areas of mathematics is to associate an object to a graph, by considering only the information of incidences between vertices and edges in a given setting. An example of this idea is to associate a point in R^n to each edge of a graph, and study the polytope defined by these points (as vertices). A famous example of this procedure is the study of symmetric edge polytopes. In this talk we will take a more topological perspective towards this idea, and consider a generalization of symmetric edge polytopes to higher dimensional simplicial complexes. This is based on joint work with Torben Donzelmann and Martina Juhnke.