  Schnyder woods are particularly elegant combinatorial structures with
numerous applications concerning planar triangulations and more generally
3-connected planar maps. We propose a simple generalization of Schnyder woods
from the plane to maps on orientable surfaces of any genus with a special
emphasis on the toroidal case. We provide a natural partition of the set of
Schnyder woods of a given map into distributive lattices depending on the
surface homology. In the toroidal case we show the existence of particular
Schnyder woods with some global properties that are useful for optimal encoding
or graph drawing purpose.
