In this paper we complete the proof of the 'equivalence' of nondiscrete R-buildings of types A 2 and C 2 , with, respectively, projective planes and generalized quadrangles with non-discrete valuation, begun in [7] . We also complete the proof of the 'equivalence' of an affine building of rank 3 with a generalized polygon with discrete valuation (by proving this for generalized hexagons), begun in [14] . We also complement the main result of [13] by proving uniqueness up to scalar multiples of

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... he weight sequences of polygons with non-discrete valuation. As an application, we produce some new explicitly defined non-discrete R-buildings, in particular a class of type A 2 with arbitrary residues.