Extending the dual of the Petersen graph

By hypotheses (a) and (c), if {i, j} is a 2-element subset of the type set I of Γ, then there are flags F of co-type {i, j}, such that res(F ) is a rank 2 geometry over the type set {i, j}, and all such {i, j}-residues are isomorphic. Hence, such a geometry Γ can be described by a diagram, in which the types (or even the exact isomorphism types) of all rank-2-residues are listed; this is often done in a graphical way. A graph D is drawn having vertices i ∈ I , one vertex for every type of objects in a hypothetical geometry belonging to the diagram, and the way two vertices i, j ∈ I are connected in the diagram reflects the type Dij of some rank 2 geometry.