  The sunspot penumbra comprises numerous thin, radially elongated filaments
that are central for heat transport within the penumbra, but whose structure is
still not clear. To investigate the fine-scale structure of these filaments, we
perform a depth-dependent inversion of spectropolarimetric data of a sunspot
very close to solar disk center obtained by Hinode (SOT/SP). We have used a
recently developed spatially coupled 2D inversion scheme which allows us to
analyze the fine structure of individual penumbral filaments up to the
diffraction limit of the telescope. Filaments of different sizes in all parts
of penumbra display very similar magnetic field strengths, inclinations and
velocity patterns. The similarities allowed us to average all these filaments
and to extract the physical properties common to all of them. This average
filament shows upflows associated with an upward pointing field at its inner,
umbral end and along its axis, downflows along the lateral edge and strong
downflows in the outer end associated with a nearly vertical, strong and
downward pointing field. The upflowing plasma is significantly hotter than the
downflowing plasma. The hot, tear-shaped head of the averaged filament can be
associated with a penumbral grain. The central part of the filament shows
nearly horizontal fields with strengths of ~1kG. The field above the filament
converges, whereas a diverging trend is seen in the deepest layers near the
head of the filament. We put forward a unified observational picture of a
sunspot penumbral filament. It is consistent with such a filament being a
magneto-convective cell, in line with recent MHD simulations. The uniformity of
its properties over the penumbra sets constraints on penumbral models and
simulations. The complex and inhomogeneous structure of the filament provides a
natural explanation for a number of long-running controversies in the
literature.
