Two conjectures regarding dense near polygons with three points on each line

AbstractWe introduce two conjectures concerning the structure of dense near polygons with three points on each line. The first conjecture deals with the whole class of such near polygons. The second conjecture deals with only those near polygons which have a nice chain of subgeometries. Although the second conjecture is implied by the first one, we introduce it because this conjecture is more likely to be proved in the near future. We prove some results which are special cases of the second conjecture and say what case is still open