During the evolution of protoplanetary disks into planetary systems we expect to detect signatures that trace mechanisms such as planet-disk interaction. Protoplanetary disks display a large variety of structures in recently published high-spatial resolution images. However, the three-dimensional morphology of these disks is often difficult to infer from the two-dimensional projected images we observe. We spatially resolve the disk around HD 34282 using VLT/SPHERE in polarimetric imaging mode. We retrieve a profile for the height of the scattering surface to create a height-corrected deprojection, which simulates a face-on orientation. The disk displays a complex scattering surface. An inner clearing or cavity extending up to r<0.28 (88 au) is surrounded by a bright inclined (i = 56 deg) ring with a position angle of 119 deg. The center of this ring is offset from the star along the minor axis with 0.07, which can be explained with a disk-height of 26 au above the mid-plane. Outside this ring, beyond its south-eastern ansa we detect an azimuthal asymmetry or blob at r ~ 0.4. At larger separation, we detect an outer disk structure that can be fitted with an ellipse, compatible with a circular ring seen at r = 0.62 (190 au) and height of 77 au. After applying a height-corrected deprojection we see a circular ring centered on the star at 88 au, while what seemed to be a separate blob and outer ring, now both could be part of a single-armed spiral. Based on the current data it is not possible to conclude decisively whether $H_{rm scat} / r$ remains constant or whether the surface is flared with at most $H_{rm scat} propto r^{1.35}$ , although we favor the constant ratio based on our deprojections. The height-corrected deprojection allows a more detailed interpretation of the observed structures, after which we discern the detection of a single-armed spiral.
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