  In the study of pattern formation in symmetric physical systems a
3-dimensional structure in thin domains is often modelled as 2-dimensional one.
We are concerned with functions in $R^3$ that are invariant under the action of
a crystallographic group and the symmetries of their projections into a
function defined on a plane. We obtain a list of the crystallographic groups
for which the projected functions have a hexagonal lattice of periods. The
proof is constructive and the result may be used in the study of observed
patterns in thin domains, whose symmetries are not expected in 2-dimensional
models, like the black-eye pattern.
