We propose a relational scheme for representing and modelling regular objects, which is based on the adjacency relations between faces and edges. In this structure, called edge-face graph, the nodes represent the faces and the arcs the edges of the corresponding object. Other topological entities, such as vertices, loops of edges, and shells, can be obtained from this relational scheme. We give a formal description of the edge-face graph, and the relationships between its properties and the topological entities of the object are analyzed in detail. Furthermore, a set of basic Euler operators based on the edge-face adjacency relation is denned, which allow the incremental manipulation of boundary representations of solid objects.