  The bright southern star L2 Pup is a particularly prominent asymptotic giant
branch (AGB) star, as its distance of 64 pc makes it the nearest of its type.
We report new adaptive optics observations of L2 Pup at visible wavelengths
with the SPHERE/ZIMPOL instrument of the VLT that confirm the presence of the
circumstellar dust disk at high inclination discovered recently by Kervella et
al. (2014b). The signature of the three-dimensional structure of the disk is
clearly observed in the map of the degree of linear polarization pL. We
identify the inner rim of the disk through its polarimetric signature at a
radius of 6 AU from the AGB star. The ZIMPOL intensity images in the V and R
bands also reveal a close-in secondary source at a projected separation of 2 AU
from the primary. The identification of the spectral type of this companion is
uncertain due to the strong reddening from the disk, but its photometry
suggests that it is a late K giant, of comparable mass to the AGB star. We
present refined physical parameters for the dust disk derived using the
RADMC-3D radiative transfer code. We also interpret the pL map using a simple
polarization model to infer the three-dimensional structure of the envelope.
Interactions between the inner binary system and the disk apparently form
spiral structures that propagate along the orthogonal axis to the disk to form
streamers. Two dust plumes propagating orthogonally to the disk are also
detected. They originate in the inner stellar system, and are possibly related
to the interaction of the wind of the two stars with the material in the disk.
Based on the morphology of the envelope of L2 Pup, we propose that this star is
at an early stage of the formation of a bipolar planetary nebula.
