  We show that the dual graph of the triangulation of the flow polytope of the
zigzag graph adorned with the length-reverse-length framing is a subgraph of a
grid graph. Through M\'esz\'aros, Morales, and Striker's bijection between
simplices of the triangulation, integer flows of a different, supplemental flow
polytope, we provide a simple numerical characterization of the adjacency
between the triangulation's simplices in terms of their corresponding integer
flows. The proofs result from the development of Postnikov and Stanley's
sequences of noncrossing bipartite trees as combinatorial objects we call
groves. We propose two new statistics derived from this construction that we
conjecture recover the $h^*$-polynomial of the flow polytope of the zigzag
graph.
