  We aim at getting high spatial resolution information on the dusty core of
bipolar planetary nebulae to directly constrain the shaping process. Methods:
We present observations of the dusty core of the extreme bipolar planetary
nebula Menzel 3 (Mz 3, Hen 2-154, the Ant) taken with the mid-infrared
interferometer MIDI/VLTI and the adaptive optics NACO/VLT. The core of Mz 3 is
clearly resolved with MIDI in the interferometric mode, whereas it is
unresolved from the Ks to the N bands with single dish 8.2 m observations on a
scale ranging from 60 to 250 mas. A striking dependence of the dust core size
with the PA angle of the baselines is observed, that is highly suggestive of an
edge-on disk whose major axis is perpendicular to the axis of the bipolar
lobes. The MIDI spectrum and the visibilities of Mz 3 exhibit a clear signature
of amorphous silicate, in contrast to the signatures of crystalline silicates
detected in binary post-AGB systems, suggesting that the disk might be
relatively young. We used radiative-transfer Monte Carlo simulations of a
passive disk to constrain its geometrical and physical parameters. Its
inclination (74 degrees $\pm$ 3 degrees) and position angle (5 degrees $\pm$ 5
degrees) are in accordance with the values derived from the study of the lobes.
The inner radius is 9$\pm$ 1 AU and the disk is relatively flat. The dust mass
stored in the disk, estimated as 1 x 10-5Msun, represents only a small fraction
of the dust mass found in the lobes and might be a kind of relic of an
essentially polar ejection process.
