  We investigate the static and dynamic properties of a weakly polydisperse
hard sphere system in the deeply supercooled state, i.e. at densities higher
than that corresponding to the mode-coupling transition. The structural
analysis reveals the emergence of icosahedral locally favoured structures,
previously only found in trace quantities. We present a new approach to probe
the shape of dynamically heterogeneous regions, which is insensitive to
particle packing effects that can hamper such analysis. Our results indicate
that the shape of the dynamically heterogeneous regions changes only weakly and
moreover hint that the often-used four-point correlation length may exhibit a
growth in excess of that which our method identifies. The growth of the size of
the dynamically heterogeneous regions appears instead to be in line with the
one of structural and dynamic propensity correlations.
