Extending the Thas-Walker construction (Q1301683)

Extending the Thas-Walker construction of spreads in \({\mathcal P} = \text{PG}(3,K)\) [see \textit{M. Walker}, Geom. Dedicata 5, 135-146 (1976; Zbl 0356.50022)] the author shows that to every spread of \({\mathcal P}\) having a unisymplecticly complemented or an elliptic regulization there corresponds a flockoid of a Lie quadric contained in the Klein quadric of \(\text{PG}(5,K)\). The converse statement is also proved.