it would seem to me that with each corner and the faces interacting with other unit cells around it, the cn would be 14
What you describe (coordination with each corners and each faces) would be for an atom at the center of the cube. But there isn't any atom sitting in the center. Remark, in the case you describe, the cube corners are too far away -> the coordination of an atom that would be sitting at the center of the cube would be 6.
To answer your question, consider the atom at the center of a cube face. How many other atoms are close to it?
- First, you have 4 atoms located at the corners of the considered face;
- Then you also have the 8 atoms located at the centers of each of the eight faces perpendicular to the considered face.
It may not be easy to see, lets take an example.
Lets consider the atom at the center of the face closest to us:
- You have the four atoms at the corners of the face which are at the distance a(√2)/2.
- You have the atom at the center of the face at the top of the cube. It is also at a distance a(√2)/2. You see it? In total there are 8 atoms equivalent to that one.