  As is well known, hard-sphere crystals of the fcc and hcp type differ very
little in their thermodynamic properties. Nonetheless, recent computer
simulations by Pronk and Frenkel indicate that the elastic response to
mechanical deformation of the two types of crystal should be quite different.
By invoking a geometrical argument put forward by R. Martin some time ago, we
suggest that this is largely due to the different symmetries of the fcc and hcp
crystal structures. Indeed, we find that elastic constants obtained by means of
computer simulations for the fcc hard-sphere crystal can be mapped onto the
equivalent ones of the hcp crystal to very high accuracy. The same procedure
applied to density functional theoretical predictions for the elastic
properties of the fcc hard-sphere crystal also produces remarkably accurate
predictions for those of the hcp hard-sphere crystal.
