Near polygons with a nice chain of sub-near polygons

In (Eur. J. Combin. 24 (2003) 631) we defined a class of near polygons and conjectured that the near 2 n -gons from this class are precisely those near polygons which satisfy the following properties: (i) every line is incident with exactly three points, (ii) every two points at distance 2 have at least two common neighbours, (iii) there exists a chain F 0 ⊂ F 1 ⊂ ⋯ ⊂ F n of geodetically closed sub-near polygons with the property that the sub-near 2 i -gon F i , i ∈ { 0 , … , n - 1 } , is big in the sub-near 2 ( i + 1 ) -gon F i + 1 . In the present paper we present a proof of this conjecture.