The Turan Density of Triple Systems Is Not Principal

The Erdős–Stone–Simonovits Theorem implies that the Turán density of a family of graphs is the minimum of the Turán densities of the individual graphs from the family. It was conjectured by Mubayi and Rödl (J. Combin. Theory Ser. A, submitted) that this is not necessarily true for hypergraphs, in particular for triple systems. We give an example, which shows that their conjecture is true.