You have a big pile of $N$ squares of lined paper. Suppose you want to glue them together, edge to edge and consistent with the lines, so the result is a surface of genus three. How many ways are there of doing it? I will show that this number is of the form $CN^d$ for a certain d which can be understood in terms of a certain graph, but where $d$ is also the complex dimension of a certain stratum in the moduli space of abelian differentials on Riemann surfaces. Further, $C$ is a multi-zeta value with a great deal of number-theoretic content.