Generalized quadrangle

In geometry, a generalized quadrangle is an incidence structure whose main feature is the lack of any (non-degenerate) triangles yet containing many quadrangles. A generalized quadrangle is by definition a polar space of rank two. They are the generalized n-gons with n = 4 and near 2n-gons with n = 2. They are also precisely the partial geometries pg(s,t,α) with α = 1.