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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  . 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  . We also complement the main result of  by proving uniqueness up to scalar multiples ofdoi:10.4310/pamq.2011.v7.n3.a11 fatcat:flll3t4iizc4tj5ei6twsfvesa