  Let $H$ be a 3-uniform hypergraph. A tournament $T$ defined on $V(T)=V(H)$ is
a realization of $H$ if the edges of $H$ are exactly the 3-element subsets of
$V(T)$ that induce 3-cycles. We characterize the 3-uniform hypergraphs that
admit realizations by using a suitable modular decomposition.
