  A solar active region (AR) is a three-dimensional magnetic structure formed
in the convection zone, whose property is fundamentally important for
determining the coronal structure and solar activity when emerged. However, our
knowledge on the detailed 3-D structure prior to its emergence is rather poor,
largely limited by the low cadence and sensitivity of previous instruments.
Here, using the 45-second high-cadence observations from the Helioseismic and
Magnetic Imager (\emph{HMI}) onboard the Solar Dynamics Observatory
(\emph{SDO}), we are able for the first time to reconstruct a 3-D datacube and
infer the detailed subsurface magnetic structure of NOAA AR 11158 and to
characterize its magnetic connectivity and topology. This task is accomplished
with the aid of the image-stacking method and advanced 3-D visualization. We
find that the AR consists of two major bipoles, or four major polarities. Each
polarity in 3-D shows interesting tree-like structure, i.e. while the root of
the polarity appears as a single tree-trunk-like tube, the top of the polarity
has multiple branches consisting of smaller and thinner flux-tubes which
connect to the branches of the opposite polarity that is similarly fragmented.
The roots of the four polarities align well along a straight line, while the
top branches are slightly non-coplanar. Our observations suggest that an active
region, even appearing highly complicated on the surface, may originate from a
simple straight flux-tube that undergoes both horizontal and vertical
bifurcation processes during its rise through the convection zone.
