Possible single-armed spiral in the protoplanetary disk around HD 34282

International audienceContext. 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. Aims. We aim to detect signatures of planet–disk interaction by studying the scattering surface of the protoplanetary disk around HD 34282. Methods. We spatially resolved the disk using the high-contrast imager VLT/SPHERE in polarimetric imaging mode. We retrieved a profile for the height of the scattering surface to create a height-corrected deprojection, which simulates a face-on orientation. Results. The detected 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°) ring with a position angle of 119°. 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 midplane. Outside this ring, beyond its southeastern 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, which is compatible with a circular ring seen at r = 0.′′62 (=190 au) and a height of 77 au. After applying a height-corrected deprojection we see a circular ring centered on the star at 88 au; what had seemed to be a separate blob and outer ring could now both be part of a single-armed spiral. Conclusions. We present the first scattered-light image of the disk around HD 34282 and resolve a disk with an inner cavity up to r ≈ 90 au and a highly structured scattering surface of an inclined disk at a large height H scat ∕ r = 0.′′29 above the midplane at the inner edge of the outer disk. Based on the current data it is not possible to conclude decisively whether H scat ∕ r remains constant or whether the surface is flared with at most H scat ∝ r 1.35 , although we favor the constant ratio based on our deprojections. The height-corrected deprojection allows for a more detailed interpretation of the observed structures, from which we discern the first detection of a single-armed spiral in a protoplanetary disk