  A rule due to Bravais of wide validity for crystals is that their surfaces
correspond to the densest planes of atoms in the bulk of the material.
Comparing a theoretical model of i-AlPdMn with experimental results, we find
that this correspondence breaks down and that surfaces parallel to the densest
planes in the bulk are not the most stable, i.e. they are not so-called bulk
terminations. The correspondence can be restored by recognizing that there is a
contribution to the surface not just from one geometrical plane but from a
layer of stacked atoms, possibly containing more than one plane. We find that
not only does the stability of high-symmetry surfaces match the density of the
corresponding layer-like bulk terminations but the exact spacings between
surface terraces and their degree of pittedness may be determined by a simple
analysis of the density of layers predicted by the bulk geometric model.
