“…2 Modified Pl ücker map and the group PO 6 (R, 3) We recall the notions of Pl ücker map, Pl ücker coordinates and Klein quadric, see [8, 2.2] and [13, p.363-367]. Let PG(3, R) = (P 3 (R), L 3 ) be the 3-dimensional projective point-line geometry, then we define for each line L ∈ L 3 a point of the projective space P 5 (R) in the following way: Choose two different points (s 0 , s 1 , s 2 , s 3 )R and (t 0 , t 1 , t 2 , t 3 )R on L and set (s 0 , s 1 , s 2 , s 3 )R ∨ (t 0 , t 1 , t 2 , t 3 )R = L → (p 0 , p 1 , p 2 , p 3 , p 4 , p 5 )R with…”