  Understanding the diversity of planets requires to study the morphology and
the physical conditions in the protoplanetary disks in which they form. We
observed and spatially resolved the disk around the ~10 Myr old protoplanetary
disk HD 100453 in polarized scattered light with SPHERE/VLT at optical and
near-infrared wavelengths, reaching an angular resolution of ~0.02", and an
inner working angle of ~0.09". We detect polarized scattered light up to ~0.42"
(~48 au) and detect a cavity, a rim with azimuthal brightness variations at an
inclination of 38 degrees, two shadows and two symmetric spiral arms. The
spiral arms originate near the location of the shadows, close to the semi major
axis. We detect a faint spiral-like feature in the SW that can be interpreted
as the scattering surface of the bottom side of the disk, if the disk is
tidally truncated by the M-dwarf companion currently seen at a projected
distance of ~119 au. We construct a radiative transfer model that accounts for
the main characteristics of the features with an inner and outer disk
misaligned by ~72 degrees. The azimuthal brightness variations along the rim
are well reproduced with the scattering phase function of the model. While
spirals can be triggered by the tidal interaction with the companion, the close
proximity of the spirals to the shadows suggests that the shadows could also
play a role. The change in stellar illumination along the rim, induces an
azimuthal variation of the scale height that can contribute to the brightness
variations. Dark regions in polarized images of transition disks are now
detected in a handful of disks and often interpreted as shadows due to a
misaligned inner disk. The origin of such a misalignment in HD 100453, and of
the spirals, is unclear, and might be due to a yet-undetected massive companion
inside the cavity, and on an inclined orbit.
