Incidence graph

An incidence graph, or Levi graph, is a graph representing the incidence relation between elements of a polytope or more generally an incidence geometry. It is a abstract representation and doesn't generally contain geometric information.

Description
An incidence graph of a incidence geometry is a simple graph with a vertex for each element of  and an edge connecting two nodes iff those elements are incident. The vertices may also be colored corresponding to their type (rank in the case of polytopes), or the coloring may be implied (especially when there are only two types of elements, for example the incidence graph of a configuration).