Characterization of some 4-gonal configurations of AHRENS-SZEKERES type

Abstract

Motivated by the Ahrens-Szekeres-Quadrangles I present a variation of the 4-gonal families method of construction introduced by Kantor in 1980. Since a long time it has been known the relation between generalized quadrangles of order (s,s) and of order (s-1,s+1). A geometrical description of this interrelation was given by Payne in 1971 and rests on the notion of regular points or rather of regular lines. In this paper I develop these connections algebraically in the hope of getting more insight into them from the group theoretical point of view. In this way I am able to characterize two classes of known 4-gonal configurations