  How, in principle, could one solve the atomic structure of a quasicrystal,
modeled as a random tiling decorated by atoms, and what techniques are
available to do it? One path is to solve the phase problem first, obtaining the
density in a higher dimensional space which yields the_averaged_ scattering
density in 3-dimensional space by the usual construction of an incommensurate
cut. A novel direct method for this is summarized and applied to an i(AlPdMn)
data set. This averaged density falls short of a true structure determination
(which would reveal the typical_unaveraged_ atomic patterns.) We discuss the
problematic validity of inferring an ideal structure by simply factoring out a
``perp-space'' Debye-Waller factor, and we test this using simulations of
rhombohedral tilings. A second, ``unified'' path is to relate the measured and
modeled intensities directly, by adjusting parameters in a simulation to
optimize the fit. This approach is well suited for unifying structural
information from diffraction and from minimizing total energies derived
ultimately from ab-initio calculations. Finally, we discuss the special
pitfalls of fitting random-tiling decagonal phases.
