  We define an extension of the geometric Lorenz model, defined on the three
sphere. This geometric model has an invariant one dimensional trefoil knot, a
union of invariant manifolds of the singularities. It is similar to the
invariant trefoil knot arising in the classical Lorenz flow near the classical
parameters. We prove that this geometric model is topologically equivalent to
the geodesic flow on the modular surface, once compactifying the latter.
