We present a transition path sampling study of the dynamics of isomerization between the S-4 and the D-2d cubic structures of the water octamer. The reaction mechanism involves a transition state characterized by a distorted face exhibiting a diagonal hydrogen bond. Analysis of an ensemble of trajectories shows that the isomerization requires concerted flips of double proton donor molecules and the interchange between dangling and bonding hydrogens in single proton donor molecules. At a total energy E = -60.5 kcal/mol, we calculated that the characteristic time for the interconversion is of the order of milliseconds. We have also investigated pathways for the melting transition at temperatures T approximate to 200 K. We find that the barrier for solid-liquid interconversions never exceeds 2k(B)T measured from the liquid side. Such transitions between liquid and solid do not involve the passage over an energetic barrier; instead, the stabilization of the liquid phase is the result of a cancellation between energetic and entropic contributions.