A general theory for dense near polygons with a nice chain of subpolygons

In [13], we determined all dense near 2n-gons of order (2, t) with a nice chain of subpolygons, i.e. a chain F0 ⊂ F1 ⊂ · · · ⊂ Fn of convex subpolygons satisfying (i) Fi, i ∈ {0, . . . , n}, is a near 2i-gon, and (ii) Fi, i ∈ {0, . . . , n− 1}, is big in Fi+1. In the present paper, we describe a method which can be used for classifying general dense near polygons with such a chain. We will use this method to determine all dense near polygons with a nice chain of subpolygons if every hex is either classical or glued. We will apply the latter result to determine all dense near octagons of order (3, t) with a nice chain of subpolygons.