  The time evolution of the medium created in heavy ion collisions can be
described by hydrodynamical models. After expansion and cooling, the hadrons
are created in a freeze-out. Their distribution describes the final state of
this medium. In particular their azimuthal asymmetry, characterized by the
elliptic flow coefficient $v_2$, is one of the most important observables in
heavy ion physics. In recent years it has been revealed that if measuring
relative to higher order event planes $\Psi_n$, higher order flow coefficients
$v_n$ for $n>2$ can be measured. This is due to initial state fluctuations,
previously not described by analytic solutions of relativistic hydrodynamics.
In this paper we show the first solutions that utilize higher order asymmetries
and thus yield realistic $v_n$ flow coefficients. It is a clear consequence of
this that different flow patterns may lead to the same observed flow
coefficients. We also compare our results to PHENIX measurements and determine
a possible parameter set corresponding to these data.
