Original Entry by Bill Leaming
All objects in the scene must be manifold, that is, be "water tight..."
Manifold models are models where the volume is well defined. They have the following properties:
1. Every edge belongs to two faces.
2. Every vertex is surrounded by one sequence of edges and faces.
3. Faces only intersect each other in common edges and vertices.
4. There is a material on only one side of a face
As a very simple example, consider the humble cube object. A cube is a manifold object; it encloses a "volume of space." Delete one face of the cube and it is no longer manifold; the "volume" is no longer fully enclosed, it "leaks..."
Another example is an "hour glass." If you were to "pinch and weld" the vertices at the "neck," the resulting object would no longer be manifold, since it is now a single object that contains two volumes of space, which is - of course - an impossibility!
All of this also means, that among other things, modelers must be very careful to have no co-linear or co-planar vertices in their geometry!