A construction of Wachspress associates to a heptagon a plane quartic curve. This has been recently reinterpreted from the point of view of positive geometry, and numerical computations suggest that a general plane quartic arises from precisely 864 heptagons. We prove this rigorously, via theta characteristics and the finite group PSL(2,7). This is joint work with Daniel Plaumann, Rainer Sinn and Jannik Weisner.
