Geometry :: Example :: Dual Three Point Geometry

Let the set of lines to be \(\mathcal{L} = \{a,b,c\}\) and the set of points to be the two element subsets of \(\mathcal{L}\). Let incidence be set membership; so the point \(\{a,b\}\) is incident with lines \(a\) and \(b\). Show this is a model for the incidence geometry. It is the dual of the model given in Three Point Geometry Example.