*Boundary Representation*, or *B-rep* for short, can be considered as
an extension to the wireframe model. The merit of a B-rep is that a solid
is bounded by its surface and has its *interior* and *exterior*.
The surface of a solid consists of a set of well-organized
faces, each of which is a piece of some surface (*.e.g.*, a surface patch).
Faces may share vertices and edges that are curve segments. Therefore, a
B-rep is an extension to the wireframe model by adding face information
to the latter.

There are two types of information in a B-rep: *topological* and
*geometric*. *Topological* information provide the relationships
among vertices, edges and faces similar to that used in a wireframe model.
In addition to connectivity, topological information also include
*orientation* of edges and faces. *Geometric* information are
usually equations of the edges and faces.

The orientation of each face is important. Normally, a face is surrounded
by a set of vertices. Using the right-handed rule, the ordering of these
vertices for describing a particular face must
guarantee that the normal vector of that face is pointing to the exterior of
the solid. Normally, the order is *counter clockwise*. If that face is
given by an equation, the equation must be rewritten so that the normal
vector at every point on the part that is being used as a face points to the
exterior of the solid. Therefore, by inspecting normal vectors one can
immediately tell the inside and outside of a solid under B-rep.
This orientation must be done for *all* faces.
The following shows 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 describe the left face,
the order should be 1, 2, 3, 4 or 2, 3, 4, 1 or 3, 4, 1, 2 or 4, 1, 2, 3.

Unfortunately, not all surfaces can be oriented this way. If the surface of
a solid can be oriented this way, it is called *orientable*; otherwise,
it is *non-orientable*. The following shows the well-known Mobius
band which is one-sided and non-orientable.