  Rooted triples, rooted binary phylogenetic trees on three leaves, are
sufficient to encode rooted binary phylogenetic trees. That is, if $\mathcal T$
and $\mathcal T'$ are rooted binary phylogenetic $X$-trees that infers the same
set of rooted triples, then $\mathcal T$ and $\mathcal T'$ are isomorphic.
However, in general, this sufficiency does not extend to rooted binary
phylogenetic networks. In this paper, we show that trinets, phylogenetic
network analogues of rooted triples, are sufficient to encode rooted binary
orchard networks. Rooted binary orchard networks naturally generalise rooted
binary tree-child networks. Moreover, we present a polynomial-time algorithm
for building a rooted binary orchard network from its set of trinets. As a
consequence, this algorithm affirmatively answers a previously-posed question
of whether there is a polynomial-time algorithm for building a rooted binary
tree-child network from the set of trinets it infers.
