  We present STAR measurements of various harmonics of three-particle
correlations in $\sqrt{s_{NN}}=200$ GeV Au+Au collisions at RHIC. The quantity
$\langle\cos(m\phi_1+n\phi_2-(m+n)\phi_3)\rangle$ is measured for inclusive
charged particles for different harmonics $m$ and $n$ as a function of
collision centrality, transverse momentum $p_T$ and relative pseudorapidity
$\Delta\eta$. These observables provide detailed information on global event
properties like correlations between event planes of different harmonics and
are particularly sensitive to the expansion dynamics of the matter produced in
the collisions. We compare our measurements to different viscous hydrodynamic
models. We argue that these measurements probe the three-dimensional structure
of the initial state and provide unique ways to constrain the transport
parameters involved in hydrodynamic modeling of heavy-ion collisions.
