Context.Fan streamers are often observed at low to mid latitudes in the corona at solar maximum, appearing narrow in latitudinal extent near the Sun, and fanning out with height, adopting an approximately linear, but not necessarily radial, configuration above ~3 $R_{⊙}$.Aims.We offer arguments to support the conjecture that such structures may sometimes consist of high density, non-uniform sheets, viewed edge-on near the Sun, and twisting to a more face-on alignment by 3 $R_{⊙}$.Methods.EUV and white light observations of a fan streamer observed on 2000/12/05 are analyzed. A simple 3D density model is used to recreate the streamer structure.Results.EIT images show a thin bright sheet at the base of the streamer. The continuation of this structure through the EIT, MLSO MKIV coronameter, and LASCO C2 fields of view, suggests that this sheet is formed mostly of open magnetic field lines. The overall large-scale appearance of the streamer is well simulated by a simple model of a twisting high-density sheet. If the twisting-sheet conjecture is valid, there is a correlation between the distribution of enhanced rays within the streamer viewed in white light, and the distribution of small regions of enhanced brightness seen on the disk in EIT 171 Å at the position of the streamer base.Conclusions.We suggest that the apparent poleward divergence of equatorial coronal rays, or threads, seen during solar maximum above active regions, may sometimes be a consequence of such a twisting sheet topology.