The southern SO+ galaxy NGC 7020 presents an unusual morphology: it includes a very regular outer ring which is completely detached and which envelops an inner ring/lens zone with an exotic hexagonal shape. The ring has a high contrast compared with those usually observed in barred galaxies, yet NGC 7020 is not obviously barred. In this paper the structure of this galaxy is studied by means of UBVRI CCD surface photometry. The photometry reveals a complex system and shows that most of the recent star formation in the galaxy has taken place in the outer ring. Two bright knots are found on the major axis of the hexagonal zone that appear to be true enhancements of old stars rather than young associations. Between these knots and the bulge there are dips in the surface brightness and a clear zone of rectangular isophotes. The combination of these rectangular isophotes and the hexagonal ones gives the impression of an "X"-shaped structure in the inner regions that bears a strong resemblance to what has been seen in the edge-on galaxy IC 4767 studied by Whitmore and Bell. This resemblance is interesting because of the suggestion by Whitmore and Bell that "X" structures could be due to accretion of matter associated with a merger or tidal encounter between an S0 and a small satellite galaxy. Except for the X, there is no clear evidence for such an encounter in the present appearance of NGC 7020, although it is a member of a sparse group. The presence of the outer ring and the non-edge-on orientation of the galaxy suggests the alternative interpretation that the hexagonal/X zone is related to an unusual type of bar or bisymmetric distortion where 4:1 and/or 6:1 resonant orbits are important in influencing the morphology. Both interpretations have difficulties which could probably be resolved with kinematic observations.