NOTE: The types and expression involving Incidence Iterators are given below for the case of vertex-on-face iteration. Analogous types and expressions can be defined for the other element types.
The tables are to be understood in the following sense:
If a Face defines the incidence iterator over vertices,
then the requirements under Optional part apply.
Analogous requirements take effect if `vertex' is replaced by another element type.
| Name | Expression | Description | 
| handle type | F::face_handle | type of the corresponding Face Handle | 
| cell type | F::Cell | Cell type of the Face, 
  short for F::grid_type::Cell. | 
| Optional part (as example) | ||
| vertex-on-face iterator | F::VertexIterator | type of the corr. VertexOnFaceIterator | 
| Name | Expression | Type requirements | return type | 
| handle | f.handle() | F::face_handle | |
| first cell | c = f.C1() | Cell | |
| second cell | c = f.C2() | Cell | |
| Optional part (as example) | |||
| vertex-on-face iteration start | f.FirstVertex() | F::VertexIterator | |
| number of incident vertices | F.NumOfVertices() | int | |
| Name | Expression | Precondition | Semantics | Postcondition | 
| handle | h = f.handle(); | f is valid | shorthand for h = f.TheGrid(). handle(f) | f == f.TheGrid(). Face(h) | 
| Optional part (as example) | ||||
| Vertex-on-Face iteration start | vf = f.FirstVertex() | f is valid | let fi point to the first vertex incident to f | vf.TheEdge() == vf.TheAnchor() == f and vf.TheGrid() == f.TheGrid() | 
| number of incident vertices | n = f.NumOfVertices() | f is valid | n is the number of vertices that are incident to f | |