Topological Geometric Information of a Solid:

The orientation of each of face is important. In general, a face is surrounded by a set of vertices. By using the right-handed rule, the ordering of these vertices for explaining a specific face must guarantee that the normal vector of that face is pointing to the exterior of the solid. In general, the order is counter clockwise. If that face is specified by an equation, the equation should be rewritten so that the normal vector at every point on the part that is being utilized as a face points to the exterior of the solid. Thus, by inspecting normal vectors one may immediately tell the inside & outside of a solid under b-rep. This orientation should be complete for all faces. The following illustrated three faces and their outward pointing normal vectors .To describe the top surface, the vertices should be 6, 7, 2, 1 or 7, 2, 1, 6 or 2, 1, 6, 7 or 1, 6, 7, 2. To depict the left face, the order must be 1, 2, 3, 4 or 2, 3, 4, 1 or 3, 4, 1, 2 or 4, 1, 2, 3.

Unluckily, not all of surfaces can be oriented this way. If the surface of a solid may be oriented this way, it is called as orientable; or else, it is non-orientable. The following shows the well-known Mobius band that is one-sided and non-orientable.