Flock generalized quadrangles and tetradic sets of elliptic quadrics of PG\((3,q)\) (Q817601)

\textit{J. A. Thas} showed in [Eur. J. Comb. 8, 441--452 (1987; Zbl 0646.51019)] that every flock of a quadratic cone of PG\((3,q\)) gives rise to a generalized quadrangle of order \((q,q^2)\). In 1999, \textit{J. A. Thas} [J. Comb. Theory, Ser. A 87, No. 2, 247--272 (1999; Zbl 0949.51003)] provided a geometrical construction of such generalized quadrangles by using a particular set of elliptic quadrics (called a tetradic set) in PG\((3,q \)). The authors of the manuscript under review characterize such tetradic sets and construct the associated generalized quadrangle synthetically from out of this characterization. As a result, this strengthens J. A. Thas' main theorem in [1999 (loc. cit.)].