  We analyze a model of quantum nets and show it has non-abelian topological
order of doubled Fibonacci type. The ground state has the same topological
behavior as that of the corresponding string-net model, but our Hamiltonian can
be defined on any lattice, has less complicated interactions, and its
excitations are dynamical, not fixed. This Hamiltonian includes terms acting on
the spins around a face, around a vertex, and special "Jones-Wenzl" terms that
serve to couple long loops together. We provide strong evidence for a gap by
exact diagonalization, completing the list of ingredients necessary for
topological order.
