  We show that hard spheres confined between two parallel hard plates pack
denser with periodic adaptive prismatic structures which are composed of
alternating prisms of spheres. The internal structure of the prisms adapts to
the slit height which results in close packings for a range of plate
separations, just above the distance where three intersecting square layers fit
exactly between the plates. The adaptive prism phases are also observed in
real-space experiments on confined sterically stabilized colloids and in Monte
Carlo simulations at finite pressure.
