Totally geodesic subgraphs of the pants complex

In recent work of Brock's, the pants graph is shown to be a combinatorial model for the completion of the Weil-Petersson metric on Teichmuller space. We prove that every Farey graph embedded in the pants graph is totally geodesic, in analogy with the extrinsic geometry of any 2-dimensional stratum inside the Weil-Petersson completion.