The number of atoms nearest to (in the neighbourhood of) an atom in the crystalline structure is called the coordination number.
CCP: This is also called Face centered cubic FCC structure.
There are 8 atoms at the 8 vertices of a unit cube in the lattice. There are 6 atoms at the centers of the 6 faces of the unit cube. The coordination number will be 12.
Around each atom (say at the center of a face F1) there are 4 atoms in the 4 corners (vertices) of the face. The distance between them is a /√2, where a = side of the unit cube.
There is a plane F1' at distance a/2 parallel to this face F1. There are 4 atoms at the centers of the four faces of unit cube, that F1' intersects. There is another plane F9 at a/2 distance on the other side of F1. It intersects 4 faces of the adjacent cube. There are 4 atoms at the centers of 4 faces.
Hence, for an atom there are 4+4+4 =12 atoms at a distance of a/√2 . Coordination number is 12.
There is an atom at the center of the cube. There are 8 atoms at the eight corner s of the cube. So the coordination number is 8, as the eight atoms at the corners (vertices) of the cube are equally distant and nearest to the atom at the center. Similarly, every atom will have 8 atoms around it.
the distance between them will be: √3 * a, where a = size of unit cube