  We recover the Newton diagram (modulo a natural ambiguity) from the link for
any surface hypersurface singularity with non-degenerate Newton principal part
whose link is a rational homology sphere. As a corollary, we show that the link
determines the embedded topological type, the Milnor fibration, and the
multiplicity of such a germ. This proves (even a stronger version of) Zariski's
Conjecture about the multiplicity for such a singularity.
