  Using pair potentials fitted to an ab--initio database, combined with
replica--exchange simulated annealing, we show the complex,
quasicrystal-related Al$_{11}$Ir$_4$ compound contains a new version of the
"pseudo-Mackay" icosahedral cluster, with non-icosahedral inner Al$_{10}$Ir
and/or Al$_9$Ir clusters that exist in various orientations and account for
partial occupancies in the reported structure. Two different compositions show
first-order transitions to orientationally ordered phases doubling the (cubic)
unit cell, which are respectively metallic and insulating.
