Topology of an arithmetic plane

An arithmetic plane is the set of points (x,y,z) in Z(3) satisfying the inequalities mu less than or equal to ax + by + cz < mu + w, where all parameters are integers and w > 0. We show that for w = \a\ + \b\ + \c\, a plane can be furnished with a canonical structure of a two-dimensional, connected, orientable combinatoric manifold without boundary, whose faces are quadrangles and whose vertices are points on the plane. This result is of interest in three-dimensional computer imaging.