  We continue our investigation into intersections of closed paths on a torus,
to further our understanding of the commutator algebra of Wilson loop
observables in 2+1 quantum gravity, when the cosmological constant is negative.
We give a concise review of previous results, e.g. that signed area phases
relate observables assigned to homotopic loops, and present new developments in
this theory of intersecting loops on a torus. We state precise rules to be
applied at intersections of both straight and crooked/rerouted paths in the
covering space $\mathbb{R}^2$. Two concrete examples of combinations of
different rules are presented.
