  A corner in a map is an edge-vertex-edge triple consisting of two distinct
edges incident to the same vertex. A corneration is a set of corners that
covers every arc of the map exactly once. Cornerations in a dart-transitive map
generalize the notion of a cycle structure in a symmetric graph. In this paper,
we study the cornerations (and associated structures) that are preserved by a
vertex-transitive group of automorphisms of the map.
