(Almost strongly minimal) generalized n-gons are constructed for all n [ges ] 3 for which the automorphism
group acts transitively on the set of ordered ordinary (n + 1)-gons contained in it, a new class of BN-pairs
thus being obtained. Through the construction being modified slightly, 2ℵ0
many non-isomorphic almost
strongly minimal generalized n-gons are obtained for all n [ges ] 3, none of which interprets an infinite group.
Furthermore, a characterization is given of all graphs whose simple cycles all have length 2n for some
n [ges ] 3.