For full topology, a set of faces covers the entire plane and no faces overlap. In this case, each edge must have a left face and a right face.
When edges are used to represent some feature such as a river, full topology is not appropriate. In the case of a river the left bank and right bank are not (topologically speaking) separate faces, because it is possible to follow the river back to its source and get to the opposite bank by walking round the end.
back to edges.html