  If ${\cal H}=(V,{\cal E})$ is a hypergraph, its edge intersection hypergraph
$EI({\cal H})=(V,{\cal E}^{EI})$ has the edge set ${\cal E}^{EI}=\{e_1 \cap e_2
\ |\ e_1, e_2 \in {\cal E} \ \wedge \ e_1 \neq e_2 \ \wedge \ |e_1 \cap e_2
|\geq2\}$. Picking up a problem from arXiv:1901.06292, for $n \ge 24$ we prove
that there is a 3-regular (and - if $n$ is even - 6-uniform) hypergraph ${\cal
H}=(V,{\cal E})$ with $\lceil \frac{n}{2} \rceil$ hyperedges and $EI({\cal H})
= C_n$.
