The image at the right shows the hexagonal lattice with its unit cell as viewed from the top.The top and bottom faces of the hexagonal unit cell are equivalent.
They each have 2 spheres contributing 1/6 and 2 spheres contributing 1/12. Therefore the total contribution to unit cell from the top and bottom faces is 1 atom.
Hold your mouse over the image to see how the vertical planes of the unit cell intersect the atoms in the middle layer. Note that these planes
- cause two portions of one sphere to be excluded
- cause the same sized portions of an adjacent sphere to be included