I attach a photo of each of the two sides of the object. The object is roughly circular, it is 27 mm across, it is 2 mm thick and it weighs 1 gram. If wet, it sinks in water (density > 1). It does not react very much to acid (not calcareous?). I found it at low tide on the beach of Vogar (SW Iceland) in late August 2017.
Is it part of some marine biota?