  The spacing distribution between Farey points has drawn attention in recent
years. It was found that the gaps $\gamma_{j+1}-\gamma_j$ between consecutive
elements of the Farey sequence produce, as $Q\to\infty$, a limiting measure.
Numerical computations suggest that for any $d\ge 2$, the gaps
$\gamma_{j+d}-\gamma_j$ also produce a limiting measure whose support is
distinguished by remarkable topological features. Here we prove the existence
of the spacing distribution for $d=2$ and characterize completely the
corresponding support of the measure.
