  We present a first, detailed study of diffractive dijet photoproduction at
the recently approved electron-ion collider (EIC) at BNL. Apart from
establishing the kinematic reaches for various beam types, energies and
kinematic cuts, we make precise predictions at next-to-leading order (NLO) of
QCD in the most important kinematic variables. We show that the EIC will
provide new and more precise information on the diffractive parton density
functions (PDFs) in the pomeron than previously obtained at HERA, illuminate
the still disputed mechanism of global vs.\ only resolved-photon factorization
breaking, and provide access to a completely new quantity, i.e. nuclear
diffractive PDFs.
