Centering small generalized polygons-projective pottery at work (Q1849942)

The paper of Polster is a nice work on generalized polygons of small order. In fact, the author makes use of the symmetry properties of the projective plane, the generalized quadrangle and the generalized hexagon of order two to provide an elementary graphical representation of these geometries. For the generalized quadrangle \(Q\) of order 2 the author's construction yields a representation based on an ordinary 5-gon \(P\). The points of \(Q\) are the subsets of \(P\) consisting of one or two vertices of \(P\). The lines of \(Q\) are the partitions of \(P\) into three subsets, each of them containing one or two elements of \(P\). Finally, the author uses this representation to obtain the well-known graphical representation of the generalized quadrangle of order 2 due to Payne.