Hyperelliptic translation surfaces and folded tori

Following constructions of McMullen [11] and Vasilyev [15] we list strict quadratic differentials on (marked) tori defined by twists of one-forms on hyperelliptic surfaces. We count the total number of twists in each genus and show that the quadratic differentials on (marked) tori are strict. Taking universal covers we obtain a variety of (non-arithmetic) lattice Panov planes [14] from genus two lattice surfaces.