  Certain fibered hyperbolic 3-manifolds admit a $\mathit{\text{layered veering
triangulation}}$, which can be constructed algorithmically given the stable
lamination of the monodromy. These triangulations were introduced by Agol in
2011, and have been further studied by several others in the years since. We
obtain experimental results which shed light on the combinatorial structure of
veering triangulations, and its relation to certain topological invariants of
the underlying manifold.
