Classification of (1,s)-geometries fully embedded in PG(n,s), for s≠2

In this paper (1,s)-geometries fully embedded in PG(n,s), for s≠2, are classified. Every proper (1,s)-geometry fully embedded in PG(n,s), for s≠2 has points the points of a cone Π[n−r−1]GQ that are not contained in the vertex Π[n−r−1], where GQ is a generalized quadrangle fully embedded in an r-dimensional subspace of PG(n,s) that is skew to π[n−r−1], and its lines are the lines that lie on this cone and that contain s+1 points of the (1,s)-geometry.