  We propose a simple generalization of Schnyder woods from the plane to maps
on orientable surfaces of higher genus. This is done in the language of angle
labelings. Generalizing results of De Fraysseix and Ossona de Mendez, and
Felsner, we establish a correspondence between these labelings and orientations
and characterize the set of orientations of a map that correspond to such a
Schnyder labeling. Furthermore, we study the set of these orientations of a
given map and provide a natural partition into distributive lattices depending
on the surface homology. This generalizes earlier results of Felsner and Ossona
de Mendez. In the toroidal case, a new proof for the existence of Schnyder
woods is derived from this approach.
