  We prove that every rational trinomial affine hypersurface admits a
horizontal polynomial curve. This result provides an explicit non-trivial
polynomial solution to a trinomial equation. Also we show that a trinomial
affine hypersurface admits a Schwartz-Halphen curve if and only if the
trinomial comes from a platonic triple. It is a generalization of
Schwartz-Halphen's Theorem for Pham-Brieskorn surfaces.
