  This article investigates the Mahler measure of a family of 2-variate
polynomials, denoted by $P_d, d\geq 1$, unbounded in both degree and genus. By
using a closed formula for the Mahler measure introduced in "Volume function
and Mahler measure of exact polynomials" (by Guilloux and March\'e), we are
able to compute $m(P_d)$, for arbitrary $d$, as a sum of the values of
dilogarithm at special roots of unity. We prove that $m(P_d)$ converges and the
limit is proportional to $\zeta(3)$, where $\zeta$ is the Riemann zeta
function.
