The self-duality of the paracyclic category is extended to the homotopy categories of a certain class of (2,1)-categories. These generalise the orbit category of a group and are associated to suitable self-dual preorders equipped with a presheaf of groups and a cosieve. The slice 2-category of equidimensional submanifolds of a compact manifold without boundary is a particular case, and for $S^1$, one recovers cyclic duality. This provides in particular a visualisation of the results of Böhm and Ştefan on the topic.