  The elegant properties of conformal mappings, when applied to two dimensional
(2D) lattices, find interesting applications in 2D foams and other cellular or
close packed structures. In particular the 2D honeycomb (whose dual is the
triangular lattice) may be transformed into various conformal patterns, which
compare approximately to experimentally realisable 2D foams. We review and
extend the mathematical analysis of such transformations, with several
illustrative examples, and an account is given of the related work in energy
minimisation problems. New results are adduced for the local curvature
generated by the transformation.
