L · L∗-geometries and Dn-buildings Original Research Article

A locally finite PG · PG∗ -geometry is a rank three incidence structure of points, lines and blocks, the block and dual point residues of which are {point,line}-systems of finite projective geometries and the line residues of which are generalized digons. We show that every locally finite thick PG · PG*-geometry satisfying two geometrical axioms (LL) and (T) is a truncation of a Dn-building. We also strongly restrict geometries satisfying (LL) and (T) over the more general diagram L · PG*.