  A gas of self-avoiding surfaces with an arbitrary polynomial coupling to the
gaussian curvature and an extrinsic curvature term can be realized in a
three-dimensional Ising bcc lattice with only three local couplings. Similar
three parameter realizations are valid also in other lattices. The relation
between the crumpling transition and the roughening is discussed. It turns out
that the mean area of these surfaces is proportional to its genus.
