On near polygons all whose hexes are dual polar spaces

One of the most fundamental results in the theory of regular near polygons is the result that every regular near 2d-gon, d 3, whose parameters s; t; ti, i 2 f0; 1;...; dg, satisfy s; t2 2 and t3 1/4 t2 2 thorn t2 is a dual polar space. The proof of that theorem heavily relies on Tits' theory of buildings, in particular on Tits' strong results on covering of chamber systems. In this paper, we give an alternative proof which only employs geometrical and algebraic combinatorial arguments