The figure below shows five computational cells. The cells, faces, and nodes are numbered. The orientation of faces is indicated by the arrows at each face.

Figure 1. Example mesh with cell, face, and node numbering.
Cell i is connected faces k that are in set \text{K} (i) . Cell i is connected nodes l that are in set \text{N} (i) . Face k is connected to nodes \text{H} (k) (head) and \text{T} (k) (tail). Face k is connected to cells \text{L} (k) (left) and \text{R} (k) (right). Cell i shares faces with neighboring cells j that are in set \text{C} (i) .
For the example above, the connectivity is given by
\text{K} (1) =\{1,2,3,4 \} , \: \text{K} (5) =\{1,5,6,7 \} , \: ...
\text{J} (1) =\{1,3,4,5 \} , \: \text{J} (5) =\{1,4,5,6 \} , \: ...
\text{H} (1) =4 , \: \text{T} (1) = 1, \text{H} (2) =3 , \: \text{T} (2) = 4,\: ...
\text{R} (1) =5 , \: \text{L} (1) = 1, \text{R} (3) =3 , \: \text{L} (3) = 1,\: ...
\text{C} (1) = \{ 2,3,4,5 \}
The orientation of face k is defined by the position of the head, \text{H} (k) , and tail, \text{T} (k) , nodes as well as the left, \text{L} (k) , and right, \text{R} (k) , cells as shown in the figure below.

Figure 2. Face orientation.