  We provide a model-theoretic classification of the countable homogeneous
$\mathbf{H}_4$-free 3-hypertournament studied by Cherlin, Hubi\v{c}ka,
Kone\v{c}n\'y, and Ne\v{s}et\v{r}il. Our main result is that the theory of this
structure is $\mathrm{SOP}_3$, $\mathrm{TP}_2$, and $\mathrm{NSOP}_4$. We offer
two proofs of this fact: one is a direct proof, and the other employs part of
the abstract machinery recently developed by Mutchnik.
