A classification of the Veldkamp lines of the near hexagon L_3 × GQ(2, 2)

Abstract

Using a standard technique sometimes (inaccurately) known as Burnside’s Lemma, it is shown that the Veldkamp space of the near hexagon L₃ × GQ(2,2) features 156 different types of lines. We also give an explicit description of each type of a line by listing the types of the three geometric hyperplanes it consists of and describing the properties of its core set, that is the subset of points of L₃ × GQ(2,2) shared by the three geometric hyperplanes in question.