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It is now generally accepted that the near-infrared excess of Herbig AeBe stars originates in the dust of a circumstellar disk. Aims. The aims of this article are to infer the radial and vertical structure of these disks at scales of order one au, and the properties of the dust grains. Methods. The program objects (51 in total) were observed with the H-band (1.6micron) PIONIER/VLTI interferometer. The largest baselines allowed us to resolve (at least partially) structures of a few tenths of an au at typical distances of a few hundred parsecs. 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