  Let $T$ be the theory of dense cyclically ordered sets with at least two
elements. We determine the classifying space of $\mathsf{Mod}(T)$ to be
homotopically equivalent to $\mathbb{CP}^\infty$. In particular,
$\pi_2(\lvert\mathsf{Mod}(T)\rvert)=\mathbb{Z}$, which answers a question in
our previous work. The computation is based on Connes' cycle category
$\Lambda$.
